The 27-year-old star is at the top of a wish list of BBC bosses who are hoping she will judge it if they get the rights to the show.
It's claimed Robbie Williams and George Michael are also being lined up to judge the show.
Cole left her role as a judge on the UK version of The X Factor to judge the US show but her spot was later given to Pussycat Dolls star Nicole Scherzinger.
A source said to UK newspaper The Sun: 'The X Factor has had a bit of a rollercoaster ride already this year and ITV fear any rival new show could blow it out of the water.
'The hype around The Voice is now so great that ITV feels it has no choice but to be in the running for it. If the BBC got it - and managed to sign Cheryl - then it could snare loads of viewers away from The X Factor.'
In the US, Christina Aguilera and Cee Lo Green are among the judges on the hit show.