Love, who is executive producer on the $60 million movie Heavier Than Heaven, has also asked Scarlett Johansson to portray her, according to British paper The Mirror.
The movie is based on Charles Cross's biography of Cobain.
A source 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. Courtney even copied Scarlett's sleek blonde movie look when she was in London for the Fashion Rocks party last year.
"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."
For more on Nirvana, check out their NME.com page.
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