The New York Post claims that there has been a "battle behind the scenes" over whether or not to hire Minaj - partly because of her diva reputation.
A source said: "There is some heated debate. There are some producers who really want her. Others have been trying to block it."
And there is also apparently resistance to the idea of hiring the pop star from the Creative Artists Agency - which represents host Ryan Seacrest and many Idol contestants, but which Minaj reportedly fired as her representation last year.
Mariah Carey was previously reported to have been unhappy about the idea of being joined on the panel by Minaj, having believed she would be the only woman judge in the forthcoming season.
We told you on Wednesday how Kanye West was reported to be in talks to join the show.
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