Despite kissing him on the lips recently and saying that she “adores him. He’s a wonderful, wonderful man,” Kate Bosworth is still denying that she’s romantically involved with Alexander Skarsgard. And it’s driving the True Blood hunk crazy. “He thinks Kate is playing hard to get. And he’s not used to that,” a source tells BettyConfidential. “Most women throw themselves at him. While he loves the chase, Kate is trying to stay more like friends.”

Romance rumors about the two started to spread last fall, when they were spotted together at the 2009 Scream Awards, reportedly held hands at a GQ magazine party and attended a screening of Fantastic Mr. Fox. But people really started talking after the two shared a long, slow romantic kiss at HBO’s Golden Globes party in January. At the time, Kate, 27, insisted she and Alex were “just friends.”

Even though she feels like she’s ready for a relationship — Kate dated actor Orlando Bloom from 2002 to 2006 and model James Rousseau for three years until they split last year — “she worries Alex is a playboy,” says the source, adding that “every girl is love struck when they meet him.”

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So Kate’s trying to keep her distance. “She’s focusing more on her career than Alex’s flirting,” says the source but it’s difficult considering the two are currently shooting the remake of the ’70s thriller Straw Dogs. Even when they’re not working together, “Alex texts and calls Kate all the time. He’s trying every trick in the book.” The 33-year-old Swedish native, who was recently linked to his True Blood co-star Evan Rachel Wood, “really likes Kate and enjoys her company,” says the insider and he will do whatever it takes to win her over.