Exhibit 5.1

April 23, 2020

Trillium Therapeutics Inc.

2488 Dunwin Drive

Mississauga, Ontario L5L 1J9

Dear Sirs/Mesdames:

Re:Trillium Therapeutics Inc. - Registration Statement on Form 3

We have acted as Canadian counsel to Trillium Therapeutics Inc. (the "Corporation"), a corporation exiting under the laws of the Province of British Columbia, in connection with the preparation and filing with the United States Securities and Exchange Commission (the "Commission") of a Registration Statement (the "Registration Statement") on Form F-3 under the United States Securities Act of 1933, as amended (the "Act"). The Registration Statement registers the issuance and sale of up to US$250,000,000 of the Corporation's common shares ("Common Shares"), First Preferred shares ("First Preferred Shares"), warrants to purchase other Securities ("Warrants"), units, comprised of one or more other Securities, in any combination ("Units"), and subscription receipts convertible into other Securities ("Subscription Receipts" and together with the Common Shares, First Preferred Shares, Warrants and Units, the "Securities"), all of which may be issued from time to time on a delayed or continuous basis pursuant to Rule 415 under the Act.

This opinion is being provided at the request of the Corporation. As Canadian counsel for the Corporation, we have examined a copy of the Registration Statement.

We are qualified to express opinions only with respect to the laws of Ontario and the federal laws of Canada applicable therein effect on the date hereof. However, we are entitled, under the National Mobility Agreement of the Federation of Law Societies (the "National Mobility Agreement"), to provide an opinion with respect to the laws of the provinces of Canada, other than Ontario, and we have provided this opinion under the National Mobility Agreement only as to the laws of the Province of British Columbia and the laws of Canada applicable therein in effect on the date hereof.

We have considered such questions of law, examined such statutes, regulations, corporate documents, records and certificates, opinions and instruments and have made such other investigations as we have considered necessary or desirable in connection with the opinions hereinafter set forth including, without limitation, a certificate of an officer of the Corporation (the "Corporate Certificate") dated the date hereof addressed to Baker & McKenzie LLP, with respect to certain factual matters.

We have relied upon the Corporate Certificate with respect to the accuracy of the factual matters contained in the Corporate Certificate, which matters have not been independently investigated or verified by us, and we have assumed that all factual statements made in the Corporate Certificate are complete, true and accurate as of the date of this opinion letter. To the extent that the Corporate Certificate, and any other certificate or document referenced herein, is based on any assumption, given in reliance on any other certificate or document, understanding or other criteria or is made subject to any limitation, qualification or exception, our opinions are also so based, given on such reliance and is so made subject.

In connection with our opinions, we have assumed (i) all information contained in all documents reviewed by us is true and correct, (ii) the genuineness of all signatures on all documents reviewed by us, (iii) the authenticity and completeness of all documents submitted to us as originals, (iv) the conformity to authentic originals of all documents submitted to us as certified or photostatic copies, (v) each natural person signing any document reviewed by us had the legal capacity to do so, none of which facts we have independently verified, (vi) no order, ruling or decision of any court or regulatory or administrative body is in effect at any relevant time that restricts the issuance of the Securities, (vii) there is no foreign law that would affect the opinion expressed herein, and (viii) at the time of the execution and delivery of any documents relating to the Securities or the offering thereof, to the extent such documents purport to constitute agreements, such documents constitute valid and binding obligations of such parties. We also have assumed the due authorization, execution and delivery of all documents where authorization, execution and delivery are prerequisites to the effectiveness of such documents.

We have also assumed that at all relevant times:

1.the Corporation has the necessary corporate power and capacity to execute, deliver and perform its obligations under the terms and conditions of any purchase, underwriting or other agreement, indenture or instrument relating to the Corporation's creation, authentication, issuance, sale and/or delivery of the Securities to which the Corporation is party (any such agreement, the "Agreement");

2.the Corporation has the necessary corporate power and capacity to authorize, create, authenticate, validly issue, sell and deliver the Securities and perform its obligations under the terms and conditions of the Securities;

3.all necessary corporate action has been taken by the Corporation to duly authorize the execution and delivery by the Corporation of the Agreement and the performance of its obligations under the terms and conditions thereof;

4.all necessary corporate action has been taken by the Corporation to duly authorize, create, authenticate, sell, deliver and validly issue the Securities and to perform its obligations under the terms and conditions of the Securities, and all of the terms and conditions relevant to the execution, delivery and issuance of the Securities in the applicable Agreement have been complied with;

5.all necessary corporate action has been taken by the Corporation to duly authorize the terms of the offering of the Securities and related matters;

6.the Agreement (i) has been duly authorized, executed and delivered by all parties thereto and such parties have the capacity to do so; (ii) constitutes a legal, valid and binding obligation of all parties thereto; (iii) is enforceable in accordance with its terms against all parties thereto; and (iv) is governed by the laws of the Province of Ontario;

7.the Securities have been duly authorized, created, authenticated, sold and delivered and validly issued by the Corporation and any other person signing or authenticating the Securities, as applicable;

8.the terms of the offering of the Securities and related matters have been duly authorized by the Corporation;

9.the execution and delivery of the Agreement and the performance by the Corporation of its obligations under the terms and conditions thereunder do not and will not conflict with and do not and will not result in a breach of or default under, and do not and will not create a state of facts which, after notice or lapse of time or both, will conflict with or result in a breach of or default under any of the terms or conditions of the notice of articles or articles of the Corporation, any resolutions of the board of directors or shareholders of the Corporation, any agreement or obligation of the Corporation, or applicable law;

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10.the authorization, creation, authentication, sale, delivery and issuance of the Securities and the Corporation's performance of its obligations under the terms and conditions of the Securities do not and will not conflict with and do not and will not result in a breach of or default under, and do not and will not create a state of facts which, after notice or lapse of time or both, will conflict with or result in a breach of or default under any of the terms or conditions of the notice of articles or articles of the Corporation, any resolutions of the board of directors or shareholders of the Corporation, any agreement or obligation of the Corporation, or applicable law; and

11.the terms of the offering of the Securities and related matters do not and will not conflict with and do not and will not result in a breach of or default under, and do not and will not create a state of facts which, after notice or lapse of time or both, will conflict with or result in a breach of or default under any of the terms or conditions of the notice of articles or articles of the Corporation, any resolutions of the board of directors or shareholders of the Corporation, any agreement or obligation of the Corporation, or applicable law.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that, upon payment for the applicable Securities provided for in the applicable Agreement and when issued, sold and delivered in accordance with such Agreement, (i) Common Shares and First Preferred Shares will be validly issued, fully paid and non-assessable shares in the capital of the Corporation, and (ii) Subscription Receipts, Warrants and Units will be validly created and issued securities of the Corporation.

This opinion letter is furnished solely for the benefit of the addressee in connection with the filing of the Registration Statement with the Commission and is not to be transmitted to any other person, nor is it to be relied upon by any other person or used for any other purpose or referred to in any public document or filed with any government agency or other person without our prior express consent. Our opinions are given as of the date of this opinion letter. Among other things, our opinions do not take into account any circumstance (including changes in law or facts or the conduct of any of the relevant parties) that may occur after that date. We assume no obligation to update or supplement any of the opinions set forth herein to reflect any changes of law or fact that may occur.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the use of our name on the cover page and under the captions "Legal Matters" and "Enforceability of Civil Liabilities" in the prospectus included in the Registration Statement. In giving such consent, we do not thereby admit that we come within the category of persons whose consent is required by the Act or the rules and regulations promulgated thereunder.

Yours very truly,

Baker & McKenzie LLP

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