The News of the World reports that the judging pair, who have been tipped to work together on the US show's panel, made it clear to ITV bosses that they will not have time to appear on both programmes.
Cowell is quoted by a 'friend' as saying: "I'm committed to the American show and I'm not going to do both."
Meanwhile an insider added: "Simon would have to produce two big shows at the same time and he and Cheryl would have to mentor and judge acts in both countries. It would just be too much for them."
However, Cowell hinted only last week on a US talkshow that he will still star in both shows. A spokesperson for Cowell also dismissed all talk of him leaving the UK show as "complete speculation".