The 52-year-old music mogul axed the British singer during auditions for the first season of the show last year amid speculations that she failed to make an impact on audiences and TV executives.
However, Rihanna, 24, is convinced that Cole, who served as a judge on the UK's 'The X Factor' before taking up the US job, was the right woman for the job and hopes she lands a similar role on the next season of rival show 'American Idol'.
"I don't know if Jennifer(Lopez) plans to stay another season or not but Cheryl would be a great replacement for her. The only thing Cheryl needs to consider is that it is so time-consuming. She was received so well on the US X Factor and most people could not really understand the decision to let her go," she said.