The 47-year-old widow of the grunge band's frontman Kurt Cobain - whose ancestors are from the same part of County Tyrone as Janet - tweeted X Factor boss Simon Cowell yesterday to suggest the idea.
She wrote: '@SimonCowell you want some Nirvana songs? @JanetJealousy is from same town as Kurt? I have the perfect idea for that, call me babe.'
The move is said to have shocked the shows bosses because getting permission from musicians for their songs to be covered by contestants on the show is usually quite difficult.
Love inherited the rights to the group's songs after Kurt Cobain killed himself back in 1994.