The Moon star has been dating actress Leslie Bibb since 2007 after they met while he was filming Frost/Nixon in Los Angeles, and they later appeared together onscreen in Iron Man 2.
But even though he is enjoying the romance, Rockwell has no plans to exchange vows with his partner.
He tells the New York Post, "I've never been married. I have a steady girlfriend I'm going with (for) three years. Will I get married? Who knows? Probably not."