The announcement came only a couple of weeks after Lythgoe had confirmed that he would be leaving American Idol to devote more time to So You Think You Can Dance -- which he produces and also serves as a judge on -- and an additional new venture with Idol creator Simon Fuller.
Lythgoe, who served as an executive producer for all of Idol's first seven editions, told the newspaper he had approved the show's use of fourth judges in the past, but only because they had all been temporary guests and not regular members of the judging panel.
"We've had lots of fourth judges, as guests, which was OK for me because they would be in one show and then you get rid of them the next," Lythgoe told the Post.
However Lythgoe comments appear to ignore the fact that Idol did also attempt to add a fourth permanent judge when he was still involved with the show. Back in 2002, American Idol had announced that New York radio personality and recording artist Angie Martinez -- who subsequently quit after only five days of auditions -- would join Abdul, Cowell and Jackson as a member of the show's second season judging panel.
Lythgoe also told the Post that he was confident that Cowell -- who reportedly seems to have stepped into a bigger role in Idol's production -- would make the right decisions to keep the show successful, and added that Cowell's work on America's Got Talent, and the UK's X-Factor had led to them both becoming successful.
However, Lythgoe also alleged that Cowell had "never produced anything on television" and should be careful not to overstep his bounds.
"At the end of the day, you have to leave it for the producers to produce, because if you're in it, you're seeing it from a completely different perspective and he's going to need to realize that," he told the Post. "Sometimes you can't see the woods through the trees and you tend to lose the most important thing, which is so often forgotten: common sense."