The Girls Aloud singer, who was axed from The X Factor USA last month, may already be in discussions for the role via her management, according to Metro.
A source said: "She is still lying low at the moment but there have been conversations with her management and things are moving forward.
"The BBC are hopeful she will commit."
It was announced yesterday that BBC One will debut The Voice in 2012, after noting the success of the US version.
BBC One controller Danny Cohen said: "I'm absolutely delighted that The Voice will be coming to the BBC. It's a big, exciting and warm-hearted series and will be a fantastic Saturday night event on BBC One."
Cheryl Cole had previously been tipped to defect to the BBC for The Voice last month. A source at the singer's record label had said: "Universal are heavily involved in recruiting judges for The Voice when it moves to the BBC and they are urging Cheryl to be the big star of that show."
Robbie Williams has also been rumoured to become a judge on the BBC One show as a possible rival to his Take That bandmate Gary Barlow, who has joined ITV's The X Factor.