Nirvana, made up of Kurt Cobain, Krist Novoselic and Dave Grohl, was an American grunge band and one of the most influential bands of the 90s. Lead singer Kurt Cobain died on the 5th of April 1994 and was not found dead until three days later by his electrician. Like Muse, Nirvana was a band which comprised of three people who had known each other since their teens.
Muse members have stated Nirvana as well with american underground grunge scene as a root influence to their music, Muse earliest song's demos have elements that are aswell heard on Nirvana's music.
A video of Muse Performing an early(1997) version of the song "showbiz" can be heard here:
Nevermind is one of Christopher Wolstenholme's favourite albums, while Dominic Howard prefers "In Utero". Howard has said that Nirvana "influenced practically everyone at some point".
On their earliest days, Muse covered Nirvana's song tourette's on a local battle of the bands.
Commonly during the Resistance Tour, the band played the riff to 'School', which was a song that was on Nirvana's debut album 'Bleach', as an outro usually to either New Born or Stockholm Syndrome. Another riff they commonly play after Stockholm Syndrome was 'Endless, Nameless' that was a hidden track on the album Nevermind. At one concert in 2017, Matt briefly played the riff to 'Breed' but wasn't fully done as a outro.
Chris in an interview for Radioundercover:
We were into Nirvana when we were younger, when we were in previous bands we did covers of their stuff, it was what got us into bands really, it was what made us want to be in bands.
A video of Muse doing riffs from Nirvana's songs School & Endless Nameless live can be seen here 
Both living former members of Nirvana, Krist Novoselic and Dave Grohl, have met Muse. Novoselic appeared on the back-stage guest-list for a 2004 Muse show and Grohl, as the Foo Fighters frontman, has played on a number of festivals with Muse. It is known that Grohl is quite a fan of Muse, especially for their live shows.