Taylor Swift & Jake Gyllenhaal: Back Together Again?

The two stars, whose brief relationship fizzled in December, arrived quietly together on Wednesday at Bound'ry, a restaurant near Swift's Nashville condo, and were led back to a table for two, according to another patron.

"They did eat," the patron tells PEOPLE. "They were cordial to one another, but not affectionate."

And another source tells PEOPLE that they seemed friendly. "There was no holding hands, but they seemed happy together," the source says. "They sat next to the fireplace just chatting away."

The two were last spotted publicly together on Dec. 9.

Swift has been lying low in Nashville in recent days, rehearsing with her band for a concert on a Royal Caribbean cruise ship, where she will perform on Friday, and for the Asian leg of her Speak Now tour, which begins in Singapore on Feb. 9.