According to the Daily Mirror, Cole blasted Cowell backstage at the US X-Factor after learning of Dannii's departure.
'She thinks that Simon should have fought for her to be kept on,' said a source. 'Cheryl is fond of the UK version, and fears it will now go downhill.'
Meanwhile, Dannii is said to be so angry about being messed around by show bosses over filming dates, that she has vowed not to return even if she is asked.
A friend told the newspaper that Dannii said: 'I can't believe this has happened to me after months of keeping my schedule clear.
'It was all going to be so perfect, but then they changed the schedules three times.
'I was so up-front with them from the beginning and they knew I wanted to do the show.
'But even if they came back to me today and said they would change things around for me, I couldn't go back. I've moved on.
'Making that decision was the hardest decision of my professional career but they left me no choice.”