The stars were reported to be clashing on the set of American Idol last week, with Carey allegedly often interrupting Minaj's critique of contestants.
© Fox / Michael Becker
Carey later quashed those rumours by quipping that "a feud takes a little longer" to develop.
Minaj has now offered her own comments to Access Hollywood on her and Carey's relationship.
"Mariah's a legend and I just want to say that… I'm sitting next to a woman who I've looked up to since I can remember enjoying music," the 'Starships' singer explained. "My mother and I bonded to Mariah and I told her that, before even American Idol."
Minaj went on to suggest that she and Carey can coexist even though they both have "strong personalities".
© Fox / Michael Becker
"Ultimately, there's respect there and I think if nothing else, it'll make for really great TV," she noted.
The star added of American Idol's new season: "It's fun. People are gonna laugh and people are gonna have a lot of fun… we just laugh ultimately at everything."
Minaj and Carey are joined by fellow judges Keith Urban and Randy Jackson for the show's new season.
American Idol returns to Fox in January 2013.
Watch Nicki Minaj's 'Starships' music video below:
