The 34-year-old actress, whose recent romance with her "Mania Days" co-star Luke Kirkby is said to have 'fizzled out', was a guest at the hunky actor's "Gravity" premiere in New York earlier this month.
The pair have enjoyed several intimate dinners after bonding at a friend's recent dinner party, reported Metro online.
"Katie and George have known each other for years. They met through her ex-husband Tom Cruise and have always got on. Katie has had a crush on him for ages. They are both single and have met up a couple of times since the dinner party," a source said.
However, insiders insist that the romance isn't serious.
"Katie and George are having a lot of fun. They are enjoying their new flirtation. He is a fun guy with buckets of charisma and Katie loves his company," the source said.
Holmes was recently romantically linked to another of Cruise's friends, Jamie Foxx, but the actor-and-singer has dismissed the speculation.
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