Exhibit 5.1

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 preparation and filing with the Securities and Exchange Commission (the “Commission”) pursuant to Rule 424(b) of the rules and regulations of the Securities Act of 1933, as amended (the “Act”), of a prospectus supplement, dated September 18, 2025 (the “Prospectus Supplement”), to the Company’s Registration Statement on Form S-3 (File No. 333-285914) filed with the Commission under the Act on March 19, 2025 (the “Registration Statement”), and the related prospectus, dated March 26, 2025, included in the Registration Statement at the time it originally became effective (the “Base Prospectus” and, together with the Prospectus Supplement, the “Prospectus”), relating to the offering by the Company of (i) 11,670,707 shares (the “Shares”) of voting common stock, par value $0.0001 per share, of the Company (the “Common Stock”), (ii) pre-funded warrants (the “Pre-Funded Warrants”) to purchase up to an aggregate of 675,000 shares of Common Stock, (iii) accompanying common warrants (the “Common Warants” and, together with the Pre-Funded Warrants, the “Warrants”) to purchase up to an aggregate of 12,345,707 shares of Common Stock and (iv) up to 13,020,707 shares of Common Stock issuable upon exercise of the Warrants (the “Warrant Shares”). The Shares and the Warrants are being sold to the Underwriters pursuant to that certain underwriting agreement, dated September 18, 2025 (the “Underwriting Agreement”), by and between the Company and TD Securities (USA) LLC, as the representative of the several underwriters named in Schedule A thereto (collectively, the “Underwriters”).

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Underwriting Agreement, the form of Pre-Funded Warrant, the form of Common Warrant, the Company’s Second Amended and Restated Certificate of Incorporation, as amended, and the Company’s Third Amended and Restated Bylaws, each as currently in effect, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters. We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies thereof.

Our opinion is limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated. Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware. We are not rendering any opinion as to compliance with any federal or state antifraud law, rule or regulation relating to securities, or to the sale or issuance thereof. Our opinion is based on these laws as in effect on the date hereof, and we disclaim any obligation to advise you of facts, circumstances, events or developments which hereafter may be brought to our attention and which may alter, affect or modify the opinion expressed herein. We express no opinion as to whether the laws of any particular jurisdiction other than those identified above are applicable to the subject matter hereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that (i) the Shares, when issued and sold against payment therefor in accordance with the Underwriting Agreement, will be validly issued, fully paid and nonassessable, (ii) the Warrants, when issued and sold against payment therefor in accordance with the Underwriting Agreement, will be valid and binding obligations of the Company and (iii) assuming sufficient authorized but unissued shares of Common Stock are available for issuance when the Warrants are exercised, the Warrant Shares, when issued, delivered and paid for in accordance with the terms of the Warrants, will be validly issued, fully paid and nonassessable.

September 19, 2025

Page 2

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus Supplement and to the filing of this opinion as an exhibit to a Current Report on Form 8-K of the Company.

Very truly yours,

/s/ Paul Hastings LLP