"It's been going on for a few months," an insider said.
MacFarlane, 38, is best known as the creator of the animated series "The Family Guy."
Clarke, 24, is a cast member of the HBO fantasy series "Game of Thrones."
MacFarlane "wants someone he is attracted to but who can have a good time and enjoy his success with," the source told UsMagazine.com. "He's actually also a 'Game of Thrones' fan!"