Cole joined The X Factor in 2008, mentoring winners Alexandra Burke and Joe McElderry in her first two years as a judge. She signed up for The X Factor USA's first season last year, but was dropped in favour of Nicole Scherzinger while auditions were being filmed.
> Cheryl Cole: 'I have never found Simon Cowell creepy'
Cowell said in an interview with GQ that he would work with 'Call My Name' singer Cole again "in a heartbeat", continuing: "I always said to her that the door is permanently open, but it is entirely up to her what she wants to do.
"To be honest with you, even though we went through that pretty horrible period, I could look Cheryl in the eye and say [that] what I did do for her in those two years really propelled her into a different league."
Cowell added that Cole was "hurt" when she was axed from The X Factor USA, but claimed that they still have a mutual understanding.
"We still have that connection. And that's why we fell out so badly, because when you're really, really close and you trust someone and you feel that person you trust has let you down - and she did feel that I had let her down - it hurts.
"It hurt me that she was upset, and I didn't want that to happen. It all ended pretty badly, to be honest with you."
Cole recently told BBC Radio 1's Chris Moyles that "a lot of rubbish" had been written about her friendship with Cowell, describing the pair as "frenemies" and admitting that she had not really given any thought to whether she would work with him again.