The actor is among the bookies' favourites to take over the part of 007 from Daniel Craig, although the former Grantchester star said that any talk of him landing the part is "pure speculation".
Norton told The Sunday Times' Culture magazine: "It's crazy. It's not real. It's speculative.
"There is no truth behind it. Unless journalists know something more than I do.
"It's bizarre and quite flattering to be even considered in that world, but beyond that? Pure speculation."
Asked how the public might react to his being cast in the role, the 34-year-old McMafia actor said: "It's really hard, as whatever I say can become a story.
"I don't know how to answer."
He added: "I love the franchise and hope Barbara Broccoli (the Bond producer) continues to make it relevant. Going into the heart of Bond's private world, as opposed to one-liners, is already progress.
"But there is more to be made, so future casting in all roles is going to be important. I don't know how you do that, because I'm not Barbara Broccoli."
Earlier in January, it was reported that bookmaker Ladbrokes had suspended betting on Norton becoming the next Bond because he was the odds-on favourite.
He is one of the most popular choices to succeed Craig, with actors including Tom Hiddleston, Sam Heughan, Richard Madden, Henry Cavill, Henry Golding and Idris Elba also in the mix.
There has been speculation that the next Bond could be a black actor, or a woman.
Craig is bowing out as 007 in No Time To Die, his fifth and final film in the franchise.
Norton is currently appearing in BBC One drama The Trial of Christine Keeler about the Profumo affair, and he is on the big screen in the new film adaptation of Little Women.