The 34-year-old actress was a guest at the premiere of Clooney's latest movie "Gravity" in New York.
"Katie and George have known each other for years. They met through her ex-husband Tom Cruise and have always got on," contactmusic.com quoted a source as saying.
"Katie has had a crush on him for ages. They're both single and have met up a couple of times since the dinner party. Katie really has her sights set on him. There is a genuine connection," the source added.
However, the source insists that the romance is not serious.
"Katie and George are having a lot of fun. They are enjoying their new flirtation. He's a fun guy with buckets of charisma and Katie loves his company," the source said.