This rumour is supported by the fact that the lady at the helm of the franchise, Barbara Broccoli, is producing Jamie Bell's latest film, 'Film Stars Don't Die In Liverpool' and is reported to be impressed by her young star's previous performances.
Jamie charmed global audiences as the screen's Billy Elliot, and has successfully transformed himself into an adult actor, with films including 'King Kong', 'Jumper' and 'Fantastic Four'.
Tom Hiddleston remains the favourite with bookies after his impressive turn in BBC drama 'The Night Manager', but Jamie will soon have his own chance to shine in a similar way. He's just finished filming '6 Days', the true story of the SAS's storming of London's Iranian Embassy in 1980, where he plays one of the UK's most elite soldiers, employed in a task that demanded bravery, cunning and skill.
Perfect timing…
However, Twitter may have something to say about all this, with the last few days seeing a concerted effort to promote Gillian Anderson into the role.
One keen fan mocked up a poster of Gillian, 007-style, something which evidently tickled the actress, who promptly shared it with her followers.
Or there's always… one of this lot (tap the first picture below to open the slideshow:
The Next James Bond Is One Of These...
Damian Lewis(01 of14)
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The first red-headed James Bond?
Idris Elba(02 of14)
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So many people have asked him about it, Idris will no longer discuss the subject. But while Pierce Brosnan remarked Bond boss Barbara Broccoli wouldn't be happy with a Black Bond, she told HuffPostUK, "I don't know what Pierce is talking about."
Tom Hardy(03 of14)
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Arguably too rugged for the corridors of Westminster where James Bond has to defend his actions, but very, very popular.
Chiwetel Ejiofor(04 of14)
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Another actor who's been asked so many times, now he just smiles when asked.
Tom Hiddleston(05 of14)
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If pouting were all that is required, Tom Hiddleston would go straight to Vauxhall Bridge.
Clive Owen(06 of14)
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Has proved he has the required steeliness in any number of big screen roles, but success Stateside might make him no longer willing to commit.
Douglas Booth(07 of14)
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No gun or martial arts skills required, he can just look at them, and wait for submission.
John Boyega(08 of14)
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What the 'Star Wars' star may lack in stature, he more than makes up for in enthusiasm and appeal. Although the Bond villains might just want to cuddle him.
Taron Egerton(09 of14)
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Proved his action hero chops in 'Kingsman: Secret Service' and signing him now would mean Barbara Broccoli and co wouldn't have to worry again for at least a decade.
Michael Fassbender(10 of14)
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Like Pierce Brosnan, Irish charm could help the 'Steve Jobs' star int the role.
Sam Claflin(11 of14)
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The 'Hunger Games' star represents the best of British.
Tom Hughes(12 of14)
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Who, you ask? Set to play Prince Albert against Jenna Coleman in the forthcoming 'Victoria' TV series, Tom has already proven himself a master of espionage in 'The Game' and 'Page Eight', both on TV. When not if he gets the call, don't say we didn't give you the heads up...
Aidan Turner(13 of14)
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Aidan has made a legion of fans with his role of Ross Poldark, but it was his surprising turn in 'And Then There Were None' that really proved he could be enigmatic and dashing. (credit:PA)
Jeremy Clarkson(14 of14)
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... or alternatively, don't say we didn't warn you.