Exhibit 5.3

To

Telefónica, S.A.

Distrito Telefónica

Ronda de la Comunicación, s/n

28050 Madrid

Spain

Madrid, 26 March 2015

Registration Statement on Form F-3 filed with the U.S. Securities and Exchange Commission by Telefónica, S.A.

Dear Sirs,

We have acted as Spanish legal counsel to Telefónica, S.A. (“Telefónica” or the “Company”), a corporation (sociedad anónima) organized under the laws of the Kingdom of Spain, in connection with the amendment to the Registration Statement on Form F-3 (the “Registration Statement”) filed by Telefónica on the date hereof with the U.S. Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), for the registration of the offer from time to time of Telefónica’s ordinary shares, nominal value €1.00 per share and rights to subscribe for ordinary shares.

1. DOCUMENTATION REVIEWED

For purposes of rendering this opinion, we have examined a copy of the following documents:

(i) A certificate of the resolutions adopted by the General Shareholders’ Meeting of Telefónica held on 18 May 2011, whereby the Board of Directors of the Company was authorized, under section 297.1.b) of the Spanish Companies Act, to increase the share capital of Telefónica, on one or more occasions and at any time, within the term of five years as from the date of said General Shareholders’ Meeting, by up to the maximum amount of 2,281,998,242.50 euros (par value),

equal to one-half of the Company’s then-current share capital, the consideration of which shall consist of cash contribution (the “Resolutions of the General Shareholder’s Meeting”);

This certificate includes a copy of the compulsory report issued by the Board of Directors of the Company in connection with the resolution proposal concerning the abovementioned authorization submitted to the General Shareholders’ Meeting of Telefónica held on 18 May 2011;

(ii) A certificate of the corporate resolutions adopted by the Board of Directors of Telefónica, on the occasion of its meeting held on 25 March 2015, executing the share capital increase of Telefónica (the “Share Capital Increase”) by the issuance of up to 281,213,184 new ordinary shares of Telefónica (the “New Shares”) to be offered and subscribed for pursuant to preferential subscription rights (the “Rights”) within the framework of a preferential subscription rights offering (the “Offering”), and passing all relevant resolutions for the purposes of the Offering and of the Transaction (the “Resolutions of the Board of Directors”);

(iii) A copy of the by-laws (Estatutos Sociales) of the Company, as they are published as of the date hereof in the corporate website of the Company;

(iv) The electronic informative report obtained from www.registradores.org on 26 March 2015 in respect of the Company.

(v) The informative report issued by the official web page disclosing information on insolvency declarations created by Royal Decree 685/2005, of 10 June 2005 (www.publicidadconcursal.es), by electronic means on 26 March 2015, showing negative results in respect of the Company; and

(vi) Registration Statement filed with the Commission.

The documents listed above shall be hereinafter jointly referred to as the “Documents”.

For purposes of issuing this opinion letter, we have made no searches or enquiries concerning the abovementioned Documents and examined no contracts or documents entered into by or affecting any of the parties to the Documents, or any other person, or any corporate records of the aforesaid, save for those searches, enquiries, contracts, instruments, documents or corporate records specified as being examined

in this opinion letter. Subject to the foregoing, we have reviewed all documents and Spanish laws that we have considered appropriate for the purposes of this opinion letter.

2. ASSUMPTIONS

In rendering the opinions expressed below, we have assumed:

(i) the genuineness of all signatures, stamps and seals appearing in the Documents, and that all the signatures contained therein correspond to the signatories thereof;

(ii) the authenticity and completeness of all Documents submitted to us as originals and the conformity with the originals and the completeness of all Documents submitted to us as copies;

(iii) that the drafts of the Documents that have been reviewed conform with the Documents finally executed;

(iv) that Telefónica have submitted to us all their relevant corporate records and proceedings, that such records and proceedings are truthful transcriptions of the resolutions passed and that they are validly executed, convened and held;

(v) that all information regarding matters of fact rendered to us by Telefónica, as well as (when appropriate) by governmental officials or public registries, is accurate and complete;

(vi) that there is nothing under any law (other than the laws of Spain) that affects our opinion; in particular, we assume all necessary compliance with applicable laws of the United States of America and the several States thereof;

(vii) the absence of fraud and the presence of good faith on the part of Telefónica;

(viii) that each of the parties to the Documents examined who is a legal entity (other than Telefónica) is duly incorporated and validly existing under the laws of its country of incorporation;

(ix) the power and authority to execute, and the due execution, by all parties to the Documents (other than Telefónica) and that such execution will bind such parties and that the performance thereof is within the capacity and powers of each of the parties thereto (other than Telefónica);

(x) that all the Documents that should have been filed with the relevant Commercial Registry of Madrid by the Company have been filed at the date hereof and that a search in respect of matters which are stated therein since the date of our search would not reveal any circumstances or the filing of Documents which would affect the conclusions reached herein, and the content of the informative reports issued by www.registradores.org by electronic means on 26 March 2015 accurately reflects the entries held at the Commercial Registry of Madrid in relation to the Company;

(xi) that the representation and warranties (other than any representation and warranties as to matters of law in connection with which we are expressing opinion herein) given by each of the parties to the Underwriting Agreement and any ancillary certificate or confirmation are in each case true, accurate and complete in all respects;

(xii) that there are no contractual or similar restrictions binding on any person which would affect the conclusions of this opinion resulting from any agreement or arrangement that is not a Document specifically examined by us for purposes of this opinion, and there are no arrangements between any of the parties to the Documents which modify or supersede any of the terms thereof;

(xiii) that the by-laws (Estatutos Sociales) of the Company which have been reviewed by us are those in force on the date hereof;

(xiv) that there are no decisions or resolutions adopted or passed by the corporate bodies of the Company revoking or amending the Company’s decisions and resolutions that we have reviewed;

(xv) that there are no documents, matters or events of a factual nature not disclosed to us which would affect the conclusions contained herein;

(xvi) that all the Documents governed by the laws of a jurisdiction other than Spain constitute legal, valid, binding and enforceable obligations of the respective parties thereto under such laws;

(xvii) that insofar as any obligation under the Documents has to be performed in, or is otherwise subject to, any jurisdiction other than Spain, it will not be illegal or ineffective by virtue of any law of, or contrary to public policy (orden público) in, that jurisdiction;

(xviii) that the Underwriting Agreement is legally binding and valid and enforceable obligations arise therefrom for all of the parties thereto other than Telefónica; and

(xix) that the Registration Statement has been filed with the Commission.

We do not represent ourselves to be familiar with the laws of any jurisdiction other than Spain as they stand at present and, therefore, we express no opinion on any question arising under any laws other than the Spanish common law (derecho común español) currently in force. In giving this opinion, we have assumed that the Documents, where expressed to be governed by the laws of a country other than Spain, are valid and binding under such laws.

Legal concepts are expressed in some of the Documents in English terms and may not be identical or equivalent to those that exist under the Spanish common law (derecho común español). Therefore, this opinion may only be relied upon provided that any issues of interpretation arising from the opinion are governed by Spanish common law (derecho común español) and brought before Spanish courts.

Our involvement in the Offering has been limited to our role as Spanish legal counsel to Telefónica and, as a consequence thereof, we assume no obligation to advise any other party to this Offering and, furthermore, we assume no obligation to advise either you or any other party of changes of law or facts that could occur after the date of the opinion, regardless of whether the change affects the legal analysis or conclusions given in this opinion.

3. OPINION

Based upon the foregoing, and subject to the additional exceptions, limitations and qualifications set forth below, and to any documents or events not disclosed to us in the course of our examination it is our opinion that:

(i) Telefónica was duly incorporated and is validly existing as a public limited company (sociedad anónima) under the laws of Spain, with full corporate power and authority to conduct its corporate purposes.

(ii) According to the on-line information made available by the Ministry of Justice in its Public Registry of Insolvency Resolutions (Registro Público de Resoluciones Concursales), and to the excerpts issued by the Commercial Registry of Madrid listed in Section 2 above, insolvency (concurso) has not been filed or declared in relation to the Company.

(iii) The New Shares will be duly authorized, fully paid, non-assessable and validly issued under the existing laws of Spain, provided that the following requirements are met: (i) approval of the Share Capital Increase pursuant to the Resolutions of the General Shareholders’ Meeting and to the Resolutions of the Board of Directors, (ii) disbursement of the subscription price of the New Shares, (iii) declaration by the Board of Directors of Telefónica, or its Executive Committee (Comisión Delegada) or an individual duly authorized for such purposes that the Share Capital Increase has been closed and subscribed, (iv) granting of the public deed evidencing the Share Capital Increase, (v) registration of the aforesaid public deed with the Commercial Registry of Madrid and (vi) record of the New Shares with the Spanish securities registration, clearing and settlement service known as Sociedad de Gestión de los Sistemas de Registro, Compensación y Liquidación de Valores, S.A. (“Iberclear”).

(iv) Upon approval of the Share Capital Increase pursuant to the Resolutions of the General Shareholders’ Meeting and to the Resolutions of the Board of Directors, the existing shareholders of Telefónica shall be entitled to exercise the Rights, provided that such Rights are not waived by the relevant holder, within a fifteen calendar day term from publication of the advertisement official notice of the capital increase in the Commercial Registry Official Gazette (Boletín Oficial del Registro Mercantil) (“BORME”).

The Rights will be duly authorized, fully paid, non-assessable and validly issued under the existing laws of Spain, provided that, following the approval of the Share Capital Increase and the publication of the official notice of the Share Capital Increase in the BORME, the Rights are recorded with Iberclear.

4. QUALIFICATIONS

The above-mentioned opinion is subject to the following qualifications:

(i) Our opinions expressed above are subject to the effects and result of the operations involved in any applicable bankruptcy, insolvency, moratorium or similar laws affecting creditors’ rights generally.

(ii) The information provided by www.registradores.org and the public registry of insolvency resolutions (www.publicidadconcursal.es) may not be completely accurate and/or up-to-date.

This opinion is being furnished by us, as Spanish counsel to Telefónica to you as a supporting document in connection with the above referenced Registration Statement.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the references to us under the caption “Validity of the Securities” contained in the Prospectus included in the Registration Statement. By so consenting, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933.

Yours faithfully,

/s/ César Albiñana Cilveti

César Albiñana Cilveti