The power-pop twins explained to Digital Spy that if they were helping Louis Walsh at the judges' houses stage of the competition, they would be on the lookout for a "superstar popstar" who was keeping it "real".
Edward said: "I want to see someone who can become bigger than the whole entire show. I know the show's really, really big, but they have to be in their own little market."
John added: "Yeah, we need to find a superstar popstar who can rival me and Edward."
On whether the show can survive without Simon Cowell, Cheryl Cole and Dannii Minogue, the Irish siblings said that Louis Walsh will be there to represent them all.
John explained: "It's great that Louis is still there because he's the original - he's going to be representing all the other judges."
Edward interjected: "Louis is going to be representing all of the California girls."
Jedward will release their new single 'Bad Behaviour' tomorrow, with their second studio album due to follow on August 15.
> Exclusive: Jedward preview tracks from new album: Video
Watch our interview with Jedward about the new series of The X Factor below: