The Daily Telegraph reports the New York franchise, which joins the British competition this season, made a pitch to Folau in a phone call recently.
The former Wallaby could be joining All Black Sonny Bill Williams in North America.
Rugby Australia and Folau announced an out-of-court settlement late last year following months of fallout stemming from Folau being sacked over his controversial social media posts, which read: “Drunks, Homosexuals, Adulterers, Liars, Fornicators, Thieves, Atheists, Idolators: Hell Awaits You. Repent! Only Jesus Saves.”