The Daily Mirror says the TV mogul has brought up the possibility of the former Girls Aloud singer returning to the talent show, after she was axed from the first series and replaced by Nicole Scherzinger.
According to the newspaper, the pair have spoken a couple of times after meeting up at Simon's Los Angeles pad in January.
A source was quoted as saying: "Simon would love to have Cheryl back. They're chatting more and more at the moment and he's hopeful she might be up for coming back.
"She's still spending a lot of time in the States and wants to move out there so it's looking more likely to be on the cards."
The second series of the US X Factor featured judges Britney Spears, LA Reid, Simon and Demi Lovato. But LA Reid and Britney have said they will not return for the next series.
Last year, Cheryl ruled herself out of the UK X Factor, saying: "It's a definite no".