The 33-year-old 'Don Jon' actor is said to be in talks to play the role of the asylum-seeking computer expert, who leaked classified intelligence details last summer, reported Deadline.
Stone and Borman have the film rights to the novel Time of the Octopus, which was written by Snowden's Russian lawyer, Anatoly Kucherena.
The novel tells the story of an American whistle-blower who travels to Russia in an attempt to gain asylum.
The producers have also bought the screen rights to 'The Snowden Files: The Inside Story of the World's Most Wanted Man', which was written by Guardian journalist Luke Harding.
Gordon-Levitt was most recently seen in 'Sin City: A Dame To Kill For'.
A documentary on Snowden, titled 'Citizenfour', will premiere at this year's BFI London Film Festival in October.
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