The 35-year-old star has been a leading contender to wield the iconic Walther PPK for most of his career, with his work in crime series McMafia leading bookies to slash odds in 2018.
In an interview to promote his new movie Nowhere Special, Norton tells Yahoo Entertainment UK that the speculation is "a little bit bemusing".
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He adds: "It has been going on for quite a long time now, so the novelty was worn off a bit. In the beginning, it was definitely quite bizarre and flattering.
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"It's never going to be not flattering to have your name included in the same sentence as James Bond. If even one person can consider that as a possibility, then it's quite cool.
"But it's been a few years now, that speculation, and it continues and remains pure speculation. It is just clickbait, I promise you that. It's nothing. There's no truth to it."
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Daniel Craig will step away from the role of James Bond after his final movie, No Time to Die, is released in cinemas after a rollercoaster of a production and multiple delays due to the coronavirus.
Speculation is naturally hotting up as to who will be Craig's replacement, with Bridgerton star Regé-Jean Page and Outlander actor Sam Heughan among the leading contenders.
"I know they're concentrating on getting the most recent movie out and seeing how they feel after that," says Norton.
"It is flattering and it never won't be, but it's nothing more than that. A little bit bemusing."
In his new film Nowhere Special, Norton plays a father with a terminal illness who spends his final months trying to find the perfect adopted family for his four-year-old son Michael, portrayed by Daniel Lamont.
"The kid is amazing, both on camera and off," says Norton. "We got on really well and genuinely had a really fun, affectionate relationship. The love you see between the father and son was real and we have that off-camera as well, so it was a pleasure."
Nowhere Special will be in UK cinemas from 16 July.
Watch: James Norton admits he got broody while filming Nowhere Special