The 32-year-old star of Grantchester and Happy Valley is currently the bookies’ favourite at 1-2 to replace Craig as James Bond.
The news came after a huge bet was placed on Norton, pushing Tom Hardy into second place.
Now the star has spoken out and claims the rumours he will take up the License to Kill after Craig’s final film in 2019 are just speculation.
Speaking with the Radio Times, Norton said: “It’s really humbling and flattering, but to have my name [talked up for Bond] next to the likes of Tom Hardy and Michael Fassbender is just mad.”
Norton continued: “If you’re thinking of putting a bet on me, keep your money in your pocket.”
The actor claims the rumours are due to Bond similarities in his new BBC series McMafia.
He added: “I did say to James Watkins, the director, ‘Are you just baiting me and stoking the rumour fire with scenes like that?’
The scene in question sees him walking around in black tie and hanging out in a casino with glamorous women.
Norton urged: “When it’s reported in the press, people assume that I’ve co-ordinated the scene, but I promise you I didn’t. The truth is that it’s total speculation.”
Craig, who turns 50 next year, starts shooting his fifth and final Bond movie in 2018.
James Bond 25 will be released in UK cinemas in November 2019.