The 27-year-old is said to be 'humiliated' after being axed from her role as a judge on the hit talent show, which will launch in the States later this year.
Cheryl was the mentor of singer Alexandra Burke, who won the UK show in 2008, beating the boy band JLS.
Speaking about her X Factor exit, the band told MTV News: 'Cheryl's one of the strongest women in this industry you know, she'll bounce back from this.
'She'll be even more popular, even better than she was before. Hopefully she'll return to the show, the UK version, and go on and win another series, she's incredible and she'll be absolutely fine.'