The 27-year-old singer has been touted for a role on the US version of the show, and according to a source, if she doesn't get on, she won't go back to the UK show.
An insider told heat magazine, 'After the US stuff, she seems to think she's too big for the UK X-Factor.
'The TV network Fox said, 'We need a J-Lo'. So Simon [Cowell] is trying to get her a Sinitta-style role. He has an influence, but it's the Fox execs who will decide.
'She'd told mates she thought she'd got the US X-Factor gig. It's a real comedown. If Simon can't get her the gig, no-one can.'
Cole's mother Joan Callaghan is said to have told her daughter that she 'doesn't think leaving the UK X-Factor is a good career move.'