There are still a few years to go until a new Bond hits the big screen.
Craig will start film Bond 25, his final outing in the role, later this year but the movie won’t be released until the end of next year.
The earliest Bond 26 is unlikely to roar into cinemas before late 2021.
After years of support for Idris Elba as the new OO7, it now looks like a two-man race between very contrasting actors.
Although he is best known for rugged but hardy tough-guy roles in Grantchester and War & Peace, Norton has also impressed with his sinister turn in Happy Valley.
McMafia was expected to cement his bid to play the iconic British superspy. Instead, underwhelming responses from viewers and critics looked likely to derail his chances.
The latest bookies figures, though, show that the public still back him as their Bond.
BoyleSports had Norton trailing at 7/1 last week but reported a huge surge in bets which have propelled him back into the lead.
Norton is now 2/1 favourite to succeed Daniel Craig, ahead of previous favourite Tom Hardy, who has drifted from 5/2 to 3/1.
BoyleSports said: “Plenty of viewers seem to have been disappointed by the McMafia finale but it hasn’t stopped them coming for James Norton as the next Bond and he’s added some spice to the 007 race, which had looked like a procession for previous favourite Tom Hardy.”
Tom Hiddleston is close behind at 7/2, followed by Idris Elba and Jack Huston on 4/1.