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Anderson, best known for directing 2007's There Will Be Blood, has been working on a screenplay for the project for some time, and Downey Jr. is said to be hoping to secure the lead role.
According to The Hollywood Reporter, Downey Jr. is said to be 'serious' about his commitment to the role, due to having a gap in his work schedule after filming on The Avengers finishes later this year.
The Iron Man actor became available after he decided to drop out playing the lead in Sam Raimi's upcoming fantasy film Oz, The Great and Powerful.
The book's plot follows a weed smoking detective who becomes embroiled in a number of mysterious occurrences during the late '60s, set in front of the ominous backdrop of the infamous Manson family trials.
Inherent Vice is due to begin filming this Fall.
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