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She has also asked Ryan Gosling to star as Cobain in the film which she is executive producing.
Heavier Than Heaven is based on a biography of the Nirvana singer, who committed suicide in 1994, to which Love contributed.
A friend of Love said: "Kirsten Dunst was rumoured to be in the frame, but Courtney really admires Scarlett and has already sent the contract out for her to sign.
"This is a labour of love for Courtney and she is putting her heart and soul into making it an accurate, credible glimpse of her life with Kurt.
"She wants the best actors to portray them - she will be on set all the time giving Scarlett and Ryan advice on what it was like being one part of the most notorious couples since Sid and Nancy. It will be explosive."
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