Taylor Swift and Jake Gyllenhaal may be a couple

After a weekend in New York City, singer Taylor Swift and "Prince of Persia" star Jake Gyllenhaal are inspiring speculation as to their couplehood. The two attended the "Saturday Night Live" broadcast in Rockefeller Center, and then Sunday reportedly brunched with another couple in Brooklyn and strolled around Park Slope.

"They showed up together" for the "SNL" airing, hosted by Swift's friend, actress Emma Stone, a source told People magazine Monday. "They walked around together backstage, but they were careful not to be seen too close." Swift, 20, initially sat down with her bodyguard, Us magazine reported, but after the lights dimmed the bodyguard got up and Gyllenhaal, 29, took the seat.

"It was hard to tell if they were together," said the People source, "but everyone was shocked that she brought him."

A witness told Us the two "chatted a lot, but no kissing or hand-holding or anything affectionate" took place.

That might have changed by Sunday. A source told Life & Style's Scene Queens column Monday, "Taylor and Jake were walking around Park Slope holding hands. They looked like a couple." Gyllenhaal's actress sister, Maggie Gyllenhaal, lives with her family in that neighborhood.

The magazines said Swift and Gyllenhaal had brunch with another couple in Brooklyn on Sunday, but did not specify where.

Swift, who has had high-profile relationships with Joe Jonas, of the Jonas Brothers, "Twilight's" Taylor Lautner and John Mayer, has a penchant for writing and recording songs about her breakups. "Every person I've fallen for, they've all been a song," she recently told Us. "That kind of justifies [the exes] being in my life."

Gyllenhaal was previously in a relationship with actress Reese Witherspoon.