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According to IndieWire, Sony Pictures and producer Scott Rudin are eager to move forward with the project, which is based on the first book in Stieg Larsson's best-selling Millennium Trilogy and the Swedish-language thriller released earlier this year.
Should Pitt commit to the movie, it will reunite him with his Se7en director David Fincher. Johnny Depp and George Clooney were actors previously mentioned in connection with the role.
Oscar-nominee Mulligan is thought to have already secured a three-film $15 million (£10 million) paycheque to play a bisexual computer hacker who teams up with a disgraced journalist to investigate a decades-old disappearance case.
Schindler's List screenwriter Steven Zaillian is currently working on adapting the novel for the Hollywood revamp.
Adaptations of Larsson's trilogy have already been completed in Sweden with original stars Noomi Rapace and Michael Nyqvist returning for Dragon Tattoo sequels The Girl Who Played With Fire and The Girl Who Kicked the Hornets' Nest.
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