The 'Rolling in the Deep' star is said to have penned the song while taking time off from touring with a chest infection.
Adele will record the track with producer Paul Epworth before submitting it to the filmmakers, The Sun reports.
"Adele is the obvious choice to record the next Bond theme," a source told the newspaper.
"The last few songs for the spy movies have hardly set the charts alight. After her success this year filmmakers know the song is almost guaranteed to be a huge hit."
Adele had previously hinted during an interview with Jonathan Ross that she might perform the new James Bond theme.
The 23rd James Bond movie will star Daniel Craig and is due for release on October 26, 2012.
Previous Bond themes have been recorded by artists including Shirley Bassey, Madonna, Wings, Garbage, Alicia Keys & Jack White, Nancy Sinatra and Duran Duran.
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Watch the Garbage 'The World Is Not Enough' music video below: