The seven time world champion racing driver said to Vanity Fair that he would have loved to be involved as he's a fan of the 1986 original.
Hamilton also revealed that he and Tom Cruise are friends: "Basically I'm a friend of Tom [Cruise]. One of the nicest people you'll ever meet. He invited me to his set years ago when he was doing Edge of Tomorrow, and then we just built a friendship over time."
He said that it was him that was chasing a role in the hit blockbuster: "When I heard the second one was coming out, I was like, 'Oh, my God, I have to ask him'.
"I said 'I don't care what role it is. I'll even sweep something, be a cleaner in the back'."
Cruise later offered Hamilton a role as a fighter pilot but he turned it down due to scheduling conflicts with his F1 commitments.
Hamilton said: "I'm a perfectionist. There just wasn't time."
The racing driver's Hollywood days aren't over though as he is involved in the making of a Formula 1 film which will star Brad Pitt. Hamilton is producing the film but there are reports he will have a small on-screen role in the project.
The untitled film will also be directed by Top Gun: Maverick director Joseph Kosinski.
Top Gun: Maverick has proved to be a huge hit and is the highest grossing movie of 2022 so far. It is also the highest grossing film of Cruise's lengthy career.
Top Gun: Maverick has also received critical acclaim, especially for its action sequences.
"That and [Steven] Spielberg's West Side Story both provided a true cinematic spectacle, the kind that I'd almost thought that I wasn't going to see anymore."
Watch below: Quentin Tarantino thought Top Gun: Maverick 'was fantastic'