As Minaj started to critique a contestant, she would reportedly be interrupted regularly by her pop diva rival during Sunday's auditions in New York City.
That caused the 29-year-old rapper to keep talking louder and louder to drown out Carey, 42, according to the report.
According to the gossip site, "the two girls just don't like each other."
The two are part of a new-look judges panel for the Fox singing competitiomn show that features country crooner Keith urban and the original judge Randy Jackson.
The newbies have a tough act to follow taking over for Jennifer Lopez and Steven Tyler, who exited early this summer after serving for the last two seasons.
It's also an increasingly crowded field with "Idol" creator Simon Cowell having corralled Britney Spears, Demi Lovato and L.A. Reid for his newer pet project, "The X-Factor." NBC's "The Voice" has an all-star lineup of its own with Blake Shelton, Cee-Lo Green, Christina Aguilera and Maroon 5's Adam Levine sitting in the swiveling chairs.
"Idol" is off to a bumpy start: TMZ reported last month that Carey hung up on producers after they told her that Minaj was in negotiations to join the show.
"American Idol" returns for the series' 12th season in January.