The 59-year-old star - who is the lead singer of R.E.M. - has revealed he reached out to the music legend shortly before his death in April 1994, when he died from a self-inflicted shotgun wound.
Asked whether he'd been planning to make music with Kurt, Michael told the BBC: "Well, yes and no. I put a project in front of him to try to pull him out of the hell he was in. I knew that he admired me and R.E.M. a lot and I came up with an idea for a project.
"I wrote him a letter, I sent him a plane ticket, I sent a car to his house to pick him up to bring him to the airport.
"We did everything we could to try to pull him out of the mental state that he was in, but that level of anguish was untouchable."
Meanwhile, a cardigan owned by Kurt recently sold at auction for $334,000.
The Nirvana frontman wore the garment during the band's MTV 'Unplugged' performance in 1993, and the stained cardigan has not been cleaned since.
The item went under the hammer in New York on Saturday (26.10.19), and is said to be the most expensive sweater ever sold at auction.
According to Darren Julien, the president of Julien's Auction, the cigarette-burned cardigan is "the holy grail of any article of clothing that he ever wore".
The music icon's custom-made Fender Mustang guitar was also sold at the auction for $340,000, having spent several years on display at the Rock and Roll Hall of Fame.