The actor, best known for his role as vampire sheriff Eric Northman on HBO's "True Blood", has been spotted with Chung on a date, reported Us magazine.
"It is serious and has really heated up. 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," a source said.
One of the new pictures on Chung's Instagram which sees her in a rose garden is reportedly taken by her rumoured boyfriend.
Skarsgard, 38, previously dated actress Kate Bosworth from 2009 to 2011. Chung, 31, split from Arctic Monkeys' frontman Alex Turner in 2011 after four-year relationship.
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