The 36-year-old, who has appeared on the British talent competition several times, would be perfect for the role, according to bosses.
It could happen if Cowell, 51, decides to focus on the US version of the show.
An insider told British newspaper The Daily Star: 'Robbie is a huge name so would naturally be a massive ratings hit. Not only that, he is also straight-talking and comical.
'We all understand that right now America is where Simon's focus has to be. There aren't many people that can fill his shoes, but Robbie just might be able to do it.'
Robbie's bandmate Gary Barlow, 40, could rival him for the job, the publication reports.