The Westlife singer has started a TV presenting career since the band broke up, and has appeared on shows including ITV1's Surprise Surprise with Holly Willoughby and ITV2's The Xtra Factor.
However, he said that he would only join if former manager Louis Walsh remained on the panel.
"Being on The X Factor judging panel would be an amazing gig and something I would thoroughly enjoy," he told The Sun.
"I would hate to replace Louis Walsh. That would never be my intention."
He added: "It's an amazing TV show and a great one to be a part of. I certainly feel that since The X Factor started I've been around it and in it an awful lot.
"I did the judges homes' with Louis, presented The Xtra Factor a few times and this will be the first series of the main X Factor show that Westlife don't perform on.
"We really have had an amazing time on The X Factor over the years so it would be great for that to continue."
[Left: Egan with wife Jodi Albert / Right: James Arthur]
Egan also said that he and wife Jodi Albert are avid viewers of the show, and tipped James Arthur to win this year's competition.
"James is definitely outstanding. I think he's probably one of the most unique artists that's been on so far and I really think he deserves to win the show.
"He's a young, cool, contemporary artist — probably the most contemporary that they have had for a long time, so it'd be good to see him win it.
"There are some other good people on there. I think Ella Henderson started off very strong and Rylan's brilliant."
Simon Cowell was recently quoted to be planning a revamp of the X Factor judging panel, including a possible return of its original lineup.