Cowell, 52, who fired Cole from the US version of singing reality show last year, said he would love to work with the 'Call My Name' hitmaker again, reported Femalefirst.
"Even though we went through that pretty horrible period, I could look Cheryl in the eye and say what I did for her in those two years propelled her into a different league. I always said to her the door is permanently open. It's entirely up to her what she wants to do," he said.
Cowell said that he wishes sacking of Cole had not happened.
"If I could reverse time it wouldn't have happened. It was an in-the-moment decision where you put your producer's hat on. I just thought she was more comfortable on the UK show. She was hurt. It all ended pretty badly, to be honest." PTI NDS
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