Katie has been single since splitting with ex-husband Tom Cruise in July of 2012. Jamie is no stranger to her ex, having worked with Tom on 2004's Collateral.
Us Weekly says Jamie and Kate's relationship "started as a fling," but "has since become a long-term attraction."
"Jamie is someone she can trust and have fun with," the magazine quotes a mutual friend. "She's getting everything from Jamie that she didn't get with Tom."
People also reports that Katie has been spotted visiting Jamie "often" at his nearby home, and that "they spend hours together" at a time.
Though despite the home visits, People says the two aren’t getting serious anytime soon.
"This is not some intense romance," a source tells the magazine. "Jamie and Katie are friends and have been for a long time. They are two adults who are attractive and single, and so apparently conclusions will be drawn. But contrary to those conclusions, they're not about to run off and make some serious commitment."
But even if the two were to become a serious item, don't expect Jamie to go public.
"I like to stay quiet, you know, with anyone that dating; that I'm really, really dating," he told ET's Nancy O'Dell in 2012 during an exclusive interview at his home in Santa Monica, Calif. "I feel like this -- If there's somebody that you're dating, the worst thing you can do is let that [points at camera] touch you. Because once that camera touches you, [it's out]. ... Yeah, we don't take time to do that [make sure the relationship is real] in Hollywood anymore."