Katie Holmes dating Alexander Skarsgard?

London: Actress Katie Holmes is reportedly dating actor Alexander Skarsgard after they grew close on the set of their movie `The Giver`.

The 35-year-old actress grew close to the 37-year-old star when they filmed `The Giver` last year and they stayed in touch afterwards and are said to have enjoyed a string of meetings recently, reportedly.

"Their flirtation was one of the worst kept secrets on set. Nobody is surprised that they`ve been spending time together. They really enjoy each other`s company," a source said.

Holmes, who has eight-year-old daughter Suri with ex-husband Tom Cruise, will be able to spend even more time with the `True Blood` star in the coming months as they will be promoting their movie.

"While it`s all quite casual at the moment, they are looking forward to spending more time with one another as they promote the film, especially as they are both single," the source added.

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