Exhibit 5.1

October 14, 2026

Jasper Therapeutics, Inc.
2200 Bridge Pkwy Suite #102
Redwood City, CA 94065

Ladies and Gentlemen:

We have acted as counsel to Jasper Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement on Form S-3 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Act”), with the Securities and Exchange Commission (the “SEC”) pursuant to Rule 415 under the Act. The Registration Statement relates to the proposed offering and sale of an aggregate of up to 284,013,011 shares (the “Shares”) of common stock, par value $0.0001 per share (“Common Stock”) issuable upon the conversion of the 4,655,951 shares of the Company’s non-voting convertible preferred stock, par value $0.0001 per share (the “Preferred Stock”), issued to certain investors in a private placement transaction (the “PIPE Offering”) pursuant to that certain securities purchase agreement, dated July 16, 2026 (the “Purchase Agreement”). This opinion is being furnished in connection with the filing of the Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus, or any prospectus filed pursuant to Rule 424(b) with respect thereto, other than as expressly stated herein with respect to the issuance of the Shares upon the conversion of the Preferred Stock.

As counsel for the Company, we have examined and relied upon the Registration Statement and the prospectus contained therein, the Purchase Agreement, and originals or copies certified or otherwise identified to our satisfaction, of the Company’s Second Amended and Restated Certificate of Incorporation (as amended, the “Charter”), the Company’s Third Amended and Restated Bylaws, the Certificate of Designation of Preferences, Rights and Limitations of Non-Voting Convertible Preferred Stock (the “Certificate of Designation”), resolutions adopted at meetings, or actions by written consent, of the board of directors of the Company (or a committee thereof) approving the Purchase Agreement and the transactions contemplated thereby, the offering and issuance of the Preferred Stock in the PIPE Offering and the preparation and filing of the Registration Statement, among other things, and such other documents, corporate records, certificates of public officials, and other instruments as we have deemed necessary for the purposes of rendering this opinion.

In our examination, we have assumed the genuineness and validity of all signatures (including, without limitation, signatures via DocuSign, eSignature or similar technology); the authenticity and completeness of all documents submitted to us as originals, and the conformity with the originals of all documents submitted to us as copies (including photostatic copies and portable document file (.pdf) copies) and the authenticity and completeness of the originals of such copies, or which we obtained from the SEC’s Electronic Data Gathering, Analysis and Retrieval (“EDGAR”) system; that each individual executing any document, whether on behalf of such individual or an entity, is legally competent to do so; the due authority of the parties signing any document on behalf of a party (other than the Company); that all public records reviewed or relied upon by us are authentic, accurate and complete; that all factual statements and information contained in any documents are true and complete; and that there has been no oral or written modification or amendments to any documents by action or omission of the parties or otherwise. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

For purposes of the opinion set forth below, we have assumed that, prior to the issuance of any Shares upon conversion of the Preferred Stock, (i) the Company will have taken all corporate action necessary to obtain the required approval of the stockholders of the Company and to make any required filing with the Secretary of State of the State of Delaware in order to amend the Charter to increase the number of authorized shares of Common Stock (and/or to effect a reverse stock split) to ensure that a sufficient number of authorized but unissued shares of Common Stock are available to permit the conversion in full of the Preferred Stock into the Shares (the “Share Authorization”) and (ii) thereafter, the Company will not issue other shares of its Common Stock, or reduce the total number of authorized shares of Common Stock under the Charter, such that the remaining number of authorized but unissued shares of Common Stock under the Charter is less than the number of the Shares.

We express no opinion concerning any laws of any state or jurisdiction other than those provisions of the General Corporation Law of the State of Delaware, including the statutory provisions, all applicable provisions of the Delaware Constitution, and the reported judicial decisions interpreting the foregoing (the “DGCL”), which, in the experience of our attorneys who are members of the bar in New York, in the exercise of customary professional diligence, are normally applicable to transactions of the type contemplated in the Purchase Agreement, but without our having made any special investigation concerning any other law, rule or regulation, in each case in effect on the date hereof. With respect to our opinion based on the DGCL, our examination has been limited to a review of such laws as reported in standard, unofficial compilations. Our opinion is based on these laws as in effect on the date hereof. No opinion is expressed herein with respect to the qualification of the Shares under the securities or blue sky laws of any state or foreign jurisdiction.

With respect to our opinions expressed below regarding the Shares issuable upon conversion of the Preferred Stock, we have assumed that at or prior to the time of issuance of such Shares, the Registration Statement will not have been modified, withdrawn or deregistered and that there will not have occurred any change in law affecting the validity of the issuance of such Shares.

Based upon the foregoing, and subject to the qualifications, assumptions (including the completion of the Share Authorization), and limitations set forth herein, we are of the opinion that the Shares issuable upon conversion of the Preferred Stock, when issued pursuant to the terms of the Charter and the Certificate of Designation, will be validly issued, fully paid and nonassessable.

The opinions expressed in this letter are limited to the matters set forth in this letter, and no other opinion should be inferred beyond the matters expressly stated. This letter is rendered as of the date hereof and we disclaim any undertaking to advise you hereafter of any facts, circumstances, events or developments hereafter occurring or coming to our attention which may alter, affect or modify the opinions expressed herein.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and to the reference to this firm under the caption “Legal Matters” in the Registration Statement. In giving such consent, we do not hereby admit that we are acting within the category of persons whose consent is required under Section 7 of the Act or the rules or regulations of the SEC thereunder (including Item 509 of Regulation S-K).

Very truly yours,

/s/ DLA Piper LLP (US)