Taylor Swift may have a new man ... Jake Gyllenhaal!

The 20-year-old singer, whose new album drops today, was spotted with the 29-year-old "Prince of Persia" star all over New York City last weekend.

Jake was reportedly part of Taylor's entourage for the SNL afterparty on Saturday -- and the two were photographed in Brooklyn together after brunch on Sunday.

We'll be going live with Taylor on TooFab at 4pm PT today for a mini-concert and Q&A at the United Nations in NYC ... maybe someone will ask her about Jake then!

Check out the livestream here!

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