She has since ruled out a return in favour of new BBC One show The Greatest Dancer.
A show source said: “Cheryl loves X Factor but she enjoyed filming the pilot for new BBC programme and loved it.
In 2017 Rita's single Anywhere reached number two in the UK charts.
The pop star has recently started dating New York rocker Andrew Watt.
Simon Cowell is said to be a big fan of the Cuban-American singer.
Another favourite among bosses is One Direction's Louis Tomlinson, who nearly became a judge two years ago.
A source said: “Louis has really matured and gained public respect for how he dealt with losing his mum.” In 2015, Louis appeared alongside Simon Cowell at the judge's house stage before he was strongly rumoured to replace Nick Grimshaw in 2016. “It was kind of surprising to see me essentially being replaced by Louis Walsh.” Pop royalty Kylie Minogue is also in contention to join the revamped panel.
A source told The Sun: "Alesha has a wealth of experience from her role on BGT and her own pop career so will do a great job filling in." She covered for Simon Cowell for the second live show, airing on Sunday October 29, after the judge in chief fell down the stairs at his home and was rushed to hospital.
However, scheduling may be an issue as she's already committed to Cowell’s BBC series The Greatest Dancer.