"I wouldn't say I don't like her. I definitely don't think she likes me," Minaj said during a Sunday night appearance on Jimmy Kimmel Live.
"I really try [to like her], because I looked up to her for a long time. So I don't want to be like hating this lady, but she just had an issue from the beginning."
When host Jimmy Kimmel asked Minaj whether she or Carey would win if they ever got into a fist fight, Minaj joked, "Well I never fight with fists [but I use] whatever weapon is handy."
"Wait, don't tell anybody I said that because then there will be another Barbara Walters interview. No, I'm kidding. I would never fight. I don't condone violence."
However, Minaj said she's been having a great time on the show thus far.
"We're having fun though. Those were the beginning episodes and of course, things happen, you guys all saw that," the rapper explained.
"But now, really, when I go to work on Idol, I'm having fun -- even at that time. Like earlier in the day I was having fun. I really genuinely enjoy going there. I like the people behind the scenes, I like the producers. We have a lot of fun. Even with Mariah and I, we really do have fun."