Jones, 34, is hosting the new series along with former Pussycat Dolls star Nicole Scherzinger while Cole and Cowell will be judges along with Paula Abdul and LA Reid.
Cowell, 51, has reportedly had words with Jones about approached Cole.
A source said to UK newspaper The People: 'Cheryl would be his dream but Simon is keen to keep business and pleasure apart.
'He can imagine the scenario now - Steve gets the hots for Cheryl and tries to pull her and then, inevitably there will be issues. Cheryl and Steve already know one another from when Steve dated Sarah [Harding - her Girls Aloud bandmate] and they get on well.
'Simon thinks Steve has got what it takes to be a star in the States, which is why he picked him to host the show, but part of his appeal is that women find him irresistible.'