During a recent interview, Reid mentioned the pop singer's name while referring to the other members of the judging panel on Fox's new reality singing show, Entertainment Weekly reports.
Fox declined to comment on the report.
Cole is an English singer who rose to fame when she was selected on a British reality show to join a pop group called Girls Aloud. She became a judge on the British version of X Factor in 2008.
The X Factor, which premieres this fall, will search the nation for undiscovered artist or group. The winning act will receive a $5 million recording contract with Syco/Sony Music.