The star has scored gargantuan sales with his most recent album Divide, and would be a logical step for producers after they chose Adele and Sam Smith for the past two movies.
What’s more, Sheeran is a hot tip with bookies to land the coveted gig.
Alex Apati of Ladbrokes said: “It’s probably one of the only things Ed Sheeran is yet to do, but rumour has it he’s already penned a theme song on the off chance he’s asked by James Bond producers to get involved – and the chances of that happening are getting slimmer by the day.”
Currently, the firm are offering odds of 7/4 for Sheeran to sing the title track.
This will be Daniel Craig’s final outing as 007, and speculation over who will replace him is relentless.
James Norton is the current pick with punters, with 5/2 odds – his work on recent BBC series McMafia only strengthening his position at the front of the pack.
Tom Hardy is a hairline behind on 3/1, with Jack Huston at 5/1 and Idris Elba at 6/1.
Aidan Turner, meanwhile, is on 8/1, while Tom Hiddleston is at 10/1.
Harry Styles has also been mentioned by some, although he is not currently listed among the top contenders.
The next Bond film follows Spectre, which was released in 2015.
Bond 25 is scheduled for release in 2019.