"The X Factor" is a talent show with a twist on what has become the standard "Idol" format, in that each of the show's four judges take an act to coach.
"Paula has a love-hate relationship with Simon, so it should be interesting," a show source told a London newspaper.
In England, the show is bigger than "Idol" and led to a bitter multimillion-dollar lawsuit between Cowell and "Idol" creator Simon Fuller.
The suit was settled late last year, with Fuller getting a piece of "The X Factor," and Cowell signing a deal worth an estimated $50 million to remain a judge on "Idol" through 2010.
A U.S. version of "The X Factor" is believed to be in development at FOX as part of Cowell's deal.
Auditions for "The X Factor" began Wednesday in England, with the show slated to debut in August.
Abdul's co-judges on "The X Factor" are believed to be Cowell, Sharon Osbourne and U.K. star Louis Walsh.