Exhibit 23.1

KPMG LLP

100 New Park Place, Suite 1400

Vaughan, ON L4K 0J3

Tel 905-265 5900

Fax 905-265 6390

www.kpmg.ca

Consent of Independent Registered Public Accounting Firm

The Board of Directors

Aptose Biosciences Inc.

We consent to the use of our report dated March 26, 2024 on the consolidated financial statements of Aptose Biosciences Inc. (the “Entity”) which comprise the consolidated statements of financial position as at December 31, 2023 and December 31, 2022, the related consolidated statements of loss and comprehensive loss, changes in shareholders’ equity and cash flows for the years then ended, and the related notes (collectively the “consolidated financial statements”), which is included in the Annual Report on Form 10 -K of the Entity for the fiscal year ended December 31, 2023.

We also consent to the incorporation by reference of such report in the Registration Statements (No. 333-257446, 333-274625, 333-228794 and 333-205158) on Form S-8, and No. 333-267801 on Form S-3 of the Entity.

We also consent to the reference to our firm under the heading “Experts” in the Registration Statements.

/s/ KPMG LLP

Chartered Professional Accountants, Licensed Public Accountants

March 26, 2024

Vaughan, Canada

KPMG LLP, an Ontario limited liability partnership and member firm of the KPMG global organization of independent member firms affiliated with KPMG International Limited, a private English company limited by guarantee. KPMG Canada provides services to KPMG LLP.