A source tells PEOPLE the two have been having "fun" together, and "it's not just a friendship at this point"
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They met in 2006 at an Oscars party. George Clooney told her he’d seen her on Dancing with the Stars. The woman, Stacy Keibler, was flattered he knew who she was – and a bit confused.

“It’s so funny,” she told PEOPLE at the time. “George Clooney came up to me, and he was like, ‘You’re so great. You should win.’ And I said, ‘You watch Dancing with the Stars?’ ”

Now, five years later, the leggy blonde, who is also a former WWE star, is the subject of romance rumors swirling around the recently single, seasoned bachelor.

Clooney, 50, who announced his split from Italian TV host Elisabetta Canalis in June, has been clocking in time with Keibler, 31, a source tells PEOPLE.

Tabloids first buzzed about a possible new lady love in the Oscar winner’s life when reports surfaced that the two enjoyed each other’s company at Clooney’s Lake Como villa in early July.

“I’m in heaven,” Keibler Tweeted July 8. The gushing continued: “I am the luckiest girl in the world,” she added the next day.

But follow-up Tweets suggested the reported Italian getaway wasn’t so one-on-one. “Our whole villa, 19 of us, are on a day trip,” she Tweeted July 13. She added, “You can’t believe anything you read and only half of what you see!”

A source tells PEOPLE that the two “have run into each other this summer.” But another source adds that they have only been “spending time together” over the last few weeks and are having “fun” – not dating. “It’s not just a friendship at this point,” the source says.

Clooney has been promoting his upcoming political drama, The Ides of March, and otherwise staying off the radar.

‘Guy’s Dream’

Dating or not, does the former wrestler have what it takes to pin down the ultimate bachelor, known for his motorcycle collection and jet-set lifestyle?

“She’s incredibly gorgeous and sweet, but she can talk sports and hold her own at the bar,” says a Keibler pal, describing her as “a guy’s dream.”

With reporting by MONICA RIZZO