is reportedly dating Swedish actor Alexander Skarsgard.
Holmes 35, grew close to Skarsgard, 37, when they filmed The Giver. They are said to have enjoyed a string of secret meetings after that.
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"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 told Grazia magazine, reports femalefirst.co.uk.
Holmes, who has an eight-year-old daughter Suri with ex-husband Tom Cruise, will be able to spend even more time with Skarsgard in the coming months as they will be promoting their movie.
The source added: "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."