Evan Rachel Wood is rumored to be dating her ''True Blood'' co-star Alexander Skarsgard.

The "Wrestler" actress is said to be so smitten with the actor she even flew to the set of his latest film this weekend so she could spend time with him.

A source told gossip blogger Perez Hilton: "Evan Rachel Wood and Alexander Skarsgard might be a thing."

"My friend is working on the set of 'Straw Dogs,' a movie starring Kate Bosworth and Alexander in Shreveport, Louisiana. Apparently, Evan Rachel Wood flew in on Friday (September 4, 2009) to be with him and they have been hooking up since they met on the 'True Blood' set. He was overheard talking about hanging out with her and actually being excited about that."

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The pair were also spotted at a local festival in Louisiana, with 22-year-old Evan taking photos with a disposable camera.

Although Alex, 33, has been linked with "Straw Dogs" actress Willa Holland, another source says his relationship with Evan has been developing in secret for some time.

The source said: "Evan and Alex met, of course, on the set of 'True Blood,' and were able to keep it low key, very underground while they were in Los Angeles."

"They never ventured out to pap friendly locations and were only sighted a few times discreetly. So far the relationship is progressing well, they're having fun together."

Evan has previously dated a string of stars including Marilyn Manson, Mickey Rourke and Edward Norton.