However, while the `True Blood` hunk is happy to spend time with Roberta Mancino, 31, he is reportedly not looking for anything serious.
A source told Life & Style magazine: "He`s been courting her and taking her out to dinner a lot. It`s not a serious relationship, but they look forward to hanging out together even more. They really like each other."
Perhaps one of the reasons Alexander wants to keep his dating options open is the recent confession by `Battleship` co-star Rihanna that she has a crush on him.
The `We Found Love` hitmaker said: "I was completely intimidated by the other actors. But I had a lot of scenes with Taylor Kitsch and he helped me out a lot along the way.
"AlexanderSkarsgard is so hot. I had to keep my game face. I could stare at him all day long. I was just watching him on set. He was really sweet."
Alexander previously dated Kate Bosworth for two years and has been linked to Charlize Theron.