Katie Holmes and Alexander Skarsgard Together in 'The Giver,' Sparks Dating Rumors

(PHOTO) REUTERS/Gus RuelasKatie Holmes photographed at the "Don't Be Afraid of the Dark" premiere in 2011

Katie Holmes and Alexander Skarsgard could be developing a new relationship, according to the latest reports.

Holmes stars alongside the "True Blood" actor in the sci-fi drama "The Giver" which filmed last year in South Africa. The stars apparently hit it off so much, that the cast and crew couldn't help but notice their friendly behavior towards one another. There are rumors that the two have supposedly stayed in touch afterwards and have enjoyed a few secret meetings recently.

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

The film, based on the Lois Lowry novel of the same title, also stars Taylor Swift, Jeff Bridges and Meryl Streep, and will premiere on Aug. 15. It is reported that the cast will be doing tours all over the world to promote the film.

A movie insider told the Belfast Telegraph that this will give Holmes and Skarsgard the perfect opportunity to spend more time with each other.

"They really enjoy each other's company. While it's all 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," said the source.

The former "Dawson's Creek" star has been romantically linked with Jamie Foxx and George Clooney since her divorce from Tom Cruise two years ago, with whom she has an 8-year-old daughter, Suri.

The star is often seen together with her daughter, and it's very evident that she dotes on her.

"I am really focused on motherhood and work right now. I didn't know how much love I had in me … Every day I discover more about this spectacular human being I get to be the mother of," she said tn a recent interview with Glamour magazine.