The actor, who worked alongside Mulligan in the action movie Drive, also asked the film's director Nicolas Winding Refn to write in a kissing scene.
He told Total Film: "Carey and I, our relationship off camera was very similar to our relationship on camera.
"We really just kind of looked at each other. It just felt good. I just liked looking at her. And I didn't want to blow it by saying anything.
"Also I really wanted to kiss so I asked the movie's director Nick if I could do it in the elevator scene before I smash a guy's head in."
Gosling recently admitted that he considers his dog to be his soulmate.