Joseph Gordon-Levitt in talks for Oliver Stone’s Edward Snowden film

One of Hollywood’s most versatile young actors could be teaming up with one of its most iconoclastic filmmakers to tell the story of National Security Agency document leaker Edward Snowden.

Joseph Gordon-Levitt is in talks to play the lead role in Oliver Stone’s upcoming narrative adaptation of Luke Harding’s nonfiction book “The Snowden Files,” The Times has confirmed. Deadline first reported the news.

The move ups the ante in the race to get a Snowden feature to the screen. Sony is developing a movie based on “No Place to Hide,” the book by Glenn Greenwald, who helped bring Snowden’s revelations to light. Stone aims to begin shooting later this year, backed by independent financing and revenue from foreign sales.

Snowden is of course a former NSA contractor who leaked thousands of classified documents about U.S. surveillance activities in June 2013. He is a polarizing figure who has been branded both a hero (by Stone and others) and a traitor (namely, by the U.S. government). He fled the U.S. after being charged with felony espionage and theft of government property, eventually finding temporary asylum in Russia.

Along with “The Snowden Files,” Stone’s film will also be based on “Time of the Octopus,” a thinly veiled novel by Snowden’s Russian lawyer, Anatoly Kucherena.

Snowden would be the latest in a string of genre-hopping performances from the 33-year-old Gordon-Levitt. In recent outings, he’s played a gambler pushing his luck in “Sin City: A Dame to Kill For,” a porn-obsessed lothario in “Don Jon” (which he also wrote and directed), Abraham Lincoln’s son in “Lincoln” and a time-traveling hired gun in “Looper.”

He’ll next appear on screen in another biopic, “The Walk,” the Robert Zemeckis-directed film about French high-wire artist Philippe Petit.

Stone is a famously outspoken filmmaker who gravitates toward political-themed projects such as “JFK,” “World Trade Center” and “W.” Upon announcing his upcoming movie in June, he called the Snowden affair “one of the greatest stories of our time.” Given his political leanings, his film is likely to be a favorable account of Snowden.

Despite the hot-button appeal, though, stories such as Snowden’s don’t always lend themselves to compelling cinematic translations. Last year, for example, the WikiLeaks thriller “The Fifth Estate” received poor reviews and grossed a disappointing $8.5 million worldwide, on an estimated $28-million budget.

In any case, Stone and Sony aren’t the only film entities interested in Snowden. Laura Poitras’ long-awaited documentary “Citizenfour” -- she and Greenwald made Snowden a household name -- will world-premiere at the upcoming New York Film Festival.

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