Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statements on Form S-8 (File No. 333-252103) and Form S-3 (File Nos. 333-257821 and 333-268652) of Compass Therapeutics, Inc. of our report dated March 21, 2024 on our audits of the consolidated financial statements of Compass Therapeutics, Inc. and subsidiaries as of December 31, 2023 and 2022 and for each of the two years in the period ended December 31, 2023, which is included in this Annual Report on Form 10-K of Compass Therapeutics, Inc. for the year ended December 31, 2023.

/s/ CohnReznick LLP

Melville, New York

March 21, 2024