The 'Fantasy' hitmaker believes her close friend would be a perfect addition to the panel because of his talent and knowledge of the music industry.
A source told HollywoodLife.com: ''Mariah would love to have her dear friend Lenny Kravitz sit next to her on the 'American Idol' judge panel. She thinks he would be the perfect choice because he is extremely talented and knows music inside and out.''
Earlier this week, it was reported that Nicki Minaj is likely to join the judging panel - a move which Mariah is said to be unhappy about because she doesn't want the contest to become a ''freak show''.
The source continued: ''Nicki on the other hand isn't established enough to qualify as a judge.
''Mariah wants a panel of bright, inspirational and constructive judges. Not some freak show! Mariah thinks Nicki will just be a distraction and it will all be about her and her outrageous behavior. Mariah will not be happy if Nicki joins the panel and she has let the producers know just how she feels!''
Meanwhile, L.A. Reid - a judge on The US 'X Factor' - has revealed Mariah signed up for the rival show on his advice.
He said: ''[Mariah and I] had a great conversation about it and I advised her that she should do it. I think it's great for her.''
The 'American Idol' judging panel has yet to be determined following the departures of Jennifer Lopez and Steven Tyler. The show's only remaining original judge Randy Jackson is expected to stay with the program but is likely to move to a mentoring role.
A host of stars have been linked with judging roles, including Nick Jonas and Kanye West.