Fuller filed the lawsuit earlier this week against Cowell, whose "X Factor" series launched last Saturday, the New York Post reported Wednesday.
"The only thing the two talent shows have in common is Cowell," Cowell said about the suit.
The celebrity judge is in Las Vegas this week filming a new season of "American Idol," for which Cowell has a three-year contract.
Both Fuller and Cowell said the legal action should not affect "American Idol."
"The action is being taken to protect our ('American Idol') format. It's not personal," said an unidentified spokesman for Fuller's 19 Entertainment company.