Taylor Swift and Jake Gyllenhaal Spotted Together in New York

Taylor Swift, right, and Jake Gyllenhaal. Getty Images

NEW YORK (CBS) Taylor Swift and Jake Gyllenhaal were spotted together over the weekend in New York - not just once, but twice.

The singer and the actor both attended the broadcast of "Saturday Night Live," which was hosted by Swift's friend Emma Stone.

PICTURES: Taylor Swift
PICTURES: Jake Gyllenhaal

"They showed up together," a source told People magazine on Monday. "They walked around together backstage, but they were careful not to be seen too close. It was hard to tell if they were together, but everyone was shocked that she brought him."

On Sunday, they were spotted together again - this time in Brooklyn's Park Slope neighborhood, which is where Gyllenhall's sister, Maggie, lives. The two had brunch with another couple and were seen strolling around the neighborhood.

The sightings led to rumors the two are dating, but a source close to Gyllenhall, 29, told People that he and Swift, 20, are just hanging out for now.

"They're cute together," the source said. "But I don't think there's anything to it. Everyone's talking about it. They hung out. But that's it. I don't think they're a couple."

A source close to Swift also downplayed the romance speculation, saying the singer, who just released a new album, isn't in a position to get involved with someone.

"Taylor is very serious about her career," the source told the magazine. "For her, it's all about the career right now. She's not really interested in getting heavily involved with anyone."

The source also predicted that if Swift does start dating, she'll look outside the entertainment business for love.

"If she does have a serious relationship, it's probably going to be with someone who's not in the industry or someone who's not a household name," the source said. "With Jake, she probably figures, why not be seen together and keep everyone guessing."