The music mogul has apparently offered the singer the choice of joining either the British or American version, with both shows due a revamp for their latest series next summer.
The US has already lost L.A. Reid from the panel, while here in the UK it's been claimed that Gary Barlow and Tulisa both face the chop.
A source claimed: "Simon is a huge admirer of Rihanna and knows she’s star quality. As well as bringing an aura to the panel thanks to her current standing in music, she is also feisty and will make great TV.
"Simon loves these sort of characters.”
According to The Sun newspaper, Simon also wants Rihanna's ex Chris Brown to join the panel of the American show next year.
Despite struggling in the ratings like its British counterpart, the US series has been given a third season on FOX next autumn.
The source told the tabloid: “The US X Factor has improved on the first season’s ratings but it’s got some way to go to reach Simon’s expectations.
"Adding Chris to the panel will certainly create a talking point.”