According to The Sun, Cobain's widow Courtney Love suggested Pattinson for the role. She allegedly also wants Scarlett Johansson to portray her in the movie.
A source said: "This is a big money deal for Courtney. She has agreed to the film on condition that she gets to decide the main aspects of the project including director, casting, screenplay and music.
"Robert has been calling and emailing her non-stop. She has been a bit wound up by his manners, but he is her number one choice to play Kurt."
The source added: "She is adamant Scarlett will play her. Scarlett is friendly with Frances Bean, her daughter with Kurt."
Love has reportedly approached Fight Club director David Fincher to helm the project, which has the working title All Apologies after the 1993 Nirvana single.
Last year, it was claimed that Love was interested in setting up Frances Bean on a date with Pattinson.