The Luther star shared a heavily filtered selfie, writing: “my name’s Elba, Idris Elba.”
Fans interpreted it as a reference to the famous spy’s catchphrase “The name’s Bond, James Bond”, and immediately responded with excitement, with one writing: “Does this... mean what I think it means......”
Another wrote: “If you’re the next Bond, it will be the first Bond film I ever see.”
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Another said: “Ticket sales for women 18-74 for James Bond movies just maxed out!”
One more wrote: “Please be 007, don’t tease us like this, get that contract signed!!”
Elba has long been rumoured to be in the running to take over the role of 007, alongside Tom Hardy, James Norton and Tom Hiddleston.
Craig will reprise the role of the spy with the licence to kill for the 25th Bond film, which will be directed by Danny Boyle.
Production is due to begin in December and it is due to be released in 2019.
A representative for Elba has been contacted for comment.