Nicki Minaj is currently on American Idol's radar to become a judge for the upcoming season. It's unclear if Nicki is even interested in the opportunity or not, however her current sponsorship with Pepsi could pose a problem that could prevent the deal from happening at all.
American Idol is sponsored by Coke, and since Coke and Pepsi are rival companies, it's unclear how Nicki's sponsorship with Pepsi could effect her the show. She's a very busy person, constantly doing concerts, shooting videos, magazines, doing interviews, etc, so who knows if she'll even have the time to put her own music aside in order to commit to American Idol.
If she were to sign a deal with the show, she'd be judging the artists alongside the great Mariah Carey.