Katie Holmes is reportedly dating her co-star in The Giver, Alexander Skarsgard.

According to Grazia magazine, the former Dawson's Creek star became close to the Swedish actor while filming the sci-fi movie last year, and they have since kept in touch.

A source told the publication: "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.

"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."

Holmes, mother to eight-year-old daughter Suri with ex-husband Tom Cruise, recently insisted that she is too busy to date at the moment.

She told America's Glamour magazine: "I am really focused on motherhood and work right now."

Alexander Skarsgard