The reality TV mogul is claimed by The Sun to be offering the pop megastar a choice of judging jobs on either the US or UK version of the talent show.
A source said: "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."
SiCo spends every Christmas at his home on Barbados, where Rihanna was born and is also planning to spend the holiday season visiting family.
And the 53-year-old is also claimed to be ready to offer RiRi's on-off BF Chris Brown a job on the panel of The X Factor USA - taking over from departing judge LA Reid.
"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," the source explained.
"Adding Chris to the panel will certainly create a talking point."