The 49-year-old actor could play the lead in Pfister's film about a man who gets sucked into a malevolent, self-aware computer, The Hollywood Reporter said.
"I'm thrilled, and feel very fortunate to have the opportunity to work with Johnny. He is a creative and intelligent artist who I feel will bring great depth to the character and the overall narrative," Pfister said.
Depp is reportedly waiting to see a final draft of writer Jack Paglen's script before fully committing.
Pfister, who won an Oscar for his work on "Inception", is "The Dark Knight Rises" director Christopher Nolan's long-time cinematography partner and has made no secret of his desire to step behind the camera as director.
His collaboration with Nolan has spanned seven films, beginning in 1999 with "Memento".
Pfister is currently considering casting the likes of Noomi Rapace, Tobey Maguire, Christoph Waltz and James McAvoy for other roles in the Warner Bros movie. PTI JCH
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Nolan and Emma Thompson will be executive producing Pfister's filmmaking debut earlier this year.
Principal photography will begin in 2013.