The actor rose to fame on Saturday Night Live, before transitioning into films with comedy hits such as Meatballs, Tootsie and Ghostbusters.
Murray has now explained that he's focused on dramatic roles like Lost in Translation and Hyde Park on Hudson because he longer identifies with Hollywood comedies.
"They're different [now]… They're just different from what I used to do," GQ.
He went on to explain: "The early movies, we just did them for fun. If they were funny, you did them. There wasn't this life-or-death thing.
"I was in movies where I would turn up, and they'd be like, 'Whaddya got?' It was like, 'Turn on two cameras and let's go'."
Murray went on to suggest that he is not totally ruling out an overtly comic role in the future.
"It's really a question I have. I think there's something that I can bring to a comedy today, but I don't know where to bring it," the star said. "I've actually thought about having a manager again. Just to clear my head and have a plan."
He concluded: "Eh, it's not that attractive to have a plan. I know that if I ever feel that I need to make a funny movie, I'll figure out how to write one. I'll get it done. If I ever get some ambition, I'm gonna get some s**t done."
His next project will be starring opposite Owen Wilson, Tilda Swinton, Adrian Brody, Jason Schwartzman and Jude Law in director Wes Anderson's Grand Budapest Hotel.
Murray's latest film Hyde Park on Hudson is now playing in the US and opens on February 1, 2013 in the UK. Watch a trailer below: