The rumoured couple was reportedly spotted on a date in Prospect Park and the Botanical Gardens in Brooklyn, New York on Friday (29May15).

A source tells Us Weekly magazine, "It is serious and has really heated up."

Another insider adds, "It's a fun relationship for both of them. She's just about as busy as he is and it's not really feasible (for them) to become a more committed couple, but the hang outs are great."

The True Blood star previously dated actress Kate Bosworth from 2009 to 2011, while Chung ended a four-year relationship with Arctic Monkeys frontman Alex Turner in 2011.