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 incorporation by reference in the registration statement (No. 333- 235730) on Form S-3 and the registration statements (No. 333-257446, No. 333-228794, and No. 333-205158) on Form S-8 of our report dated March 22, 2022, with respect to the consolidated financial statements of Aptose Biosciences Inc. which comprise the consolidated statements of financial position as at December 31, 2021 and December 31, 2020, the related consolidated statements of loss and comprehensive loss, changes in shareholders’ equity and cash flows for each of the years in the two-year period ended December 31, 2021, and the related notes, which report appears in the December 31, 2021 annual report on Form 10-K of Aptose Biosciences Inc.

/s/ KPMG LLP

Chartered Professional Accountants, Licensed Public Accountants
March 22, 2022
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.