The 24-year-old singer would be the first repeat Bond singer since Shirley Bassey sang 'Goldfinger', 'Diamonds Are Forever' and 'Moonraker', reported Daily Mirror online.
Craig, 44, has also reportedly pushed bosses at MGM to sign up 'Skyfall' director Sam Mendes for the next film.
"Daniel wants to keep the winning team. He loved Adele and wants her back alongwith director Sam Mendes," a source said.
Adele's 'Skyfall' track is predicted to score a nomination for Best Original Song at the 85th annual Academy Awards.
Adele, who gave birth to a son last October, will reportedly make her first public appearance at the award ceremony in February.
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