The 'Atonement' star is hotly-tipped to portray the Nirvana frontman, who committed suicide in 1994, in a film about his life, which is due to be produced by Cobain's widow Courtney Love.
A source said: "James is making a big impact in Hollywood at the moment. Hollywood bosses are convinced he is the perfect choice to play Kurt Cobain."
The film will be largely based on Charles Cross' biography 'Heavier than Heaven'.
Cobain's unpublished journals will also be used to fill in personal details for the screenplay, which is being penned by 'Troy' writer David Benioff.
Cobain enjoyed massive success fronting Nirvana with bassist Krist Novoselic and drummer Dave Grohl in the early 90s with hits like 'Smells Like Teen Spirit' and 'Come As You Are', but his life was dogged by depression and drug use.
He was just 27 when he shot himself, leaving behind Courtney and their daughter Frances Bean Cobain, now 16.