The X Factor judge is keen for Roberts to sign a one-album deal but is worried he may be tempted by the lead role in the Phantom of the Opera sequel in the West End, according to The Sun.
A source commented: "Simon is relaxed about Rhydian doing Phantom but he wants to make sure he gets his record deal done first.
"That way Andrew Lloyd Webber has to work around Simon rather than the other way round."
Roberts has been quoted as saying: "Andrew and I have communicated. My ambition is to play the Phantom at the end of next year."
Cowell is also reportedly considering offering third-place finalists Same Difference a recording contract.