Craig is sticking around for one final James Bond movie in 2019, but who will replace him as 007?
For much of this year Hardy has been the firm favourite, however Norton has now taken the lead.
Coral Bookmakers has seen a huge gamble made on the McMafia star in the last day, placing him at odds-on with 1-2 to be the next Bond.
A spokesman said: “James Norton has all the credentials to be 007, so it is easy to see why punters are backing the actor to play the next James Bond – where he is now odds-on to replace Daniel Craig following a huge gamble in the last 24 hours.”
Meanwhile Hardy is currently the second favourite to take up the License to Kill at 7-2.
He is followed by Jack Huston at 4-1, Aidan Turner at 6-1, Tom Hiddleston at 12-1 and Idris Elba at 14-1.
Additionally the odds on the next James Bond being played by a female actress are at 5-1.
Just before Christmas Norton spoke out on the rumours he was set to replace Craig as Bond.
The actor said: “It’s lovely, wonderful and complimentary to be involved in that conversation but it’s just a rumour mill and that’s as far as it goes.
“I hope Daniel Craig does five more movies and can keep the rumours on himself. I’m a big fan of his and – selfishly – I’d like him to carry on.”
Norton stars in BBC drama McMafia next week, which sees him wear black tie while socialising with women at a casino, fights villains and is seen in Craig-style swimming trunks in the sea.