Charlize Theron and Alexander Skarsgrd have sparked rumours they are dating after they were spotted getting cosy at a bar.

The pair were seen together at the Gym Sportsbar, a gay nightspot in Hollywood, according to the National Enquirer.

A source told the publication "it was clear they were a couple" as they were holding hands and staring into each other's eyes on the patio after ordering two beers.

"People said hello, and they were really nice," the source added.

"After about 45 minutes, they left with their arms around each other and drove off in the same car."

Monster star Charlize, 36, was previously linked with Ryan Reynolds last summer following her 2010 break-up from actor Stuart Townsend after nine years.

Alexander, who is best known for his role as vampire Eric Northman in True Blood, split from Kate Bosworth last year. Since returning to the dating scene, he was also seen getting "friendly" with Elizabeth Olsen at the post-Oscars Vanity Fair party.

A source claims Charlize is "crazy" for the 35-year-old actor and he is equally "nuts" about the blonde beauty.

"They've both been through some bad break-ups and want to keep the romance to themselves for the time being. They figured no one would notice them at a gay bar," the insider said.

It has been claimed both Charlize and Alexander have been "scarred" by past relationships.

"Now, with each other, they will perhaps find love and happiness they both deserve," a friend added.