"Cheryl has been an instant hit with viewers and contestants," the Mirror quoted a studio insider as saying.
"She initially signed a one-year deal as she wasn't sure how she would fare and Simon didn't want to commit to an unknown quantity. Now he's desperate to get her for a new series and put pen to paper. He realises he will have to fight to keep her as Girls Aloud are in talks to do a US tour. So Simon needs to act fast and get her to sign before she has unavoidable commitments. As part of the package there's talk of involving her in another of Simon's shows. Cheryl is flattered," the insider added.
If Cole accepts the offer, it would put her ahead of Dannii Minogue, who is now in her second series, by 100,000 pounds.