The computer professional leaked classified information from the NSA to the mainstream media, starting in June 2013.
The film, which is directed by Oliver Stone, already stars Joseph Gordon-Levitt and Shailene Woodley, reported TheWrap.
Leo, Quinto and Wilkinson might play Laura Poitras, Glenn Greenwald and Ewen MacAskill respectively in 'The Snowden Files'.
Poitras is the director of Oscar-nominated Snowden documentary 'Citizenfour', which was also a part of the whistleblower's revelations.
Greenwald is a lawyer/journalist, who was chosen by Snowden to leak information to. MacAskill is a contributor at The Guardian who helped break Snowden's stories about mass surveillance.
Scott Eastwood has also joined the movie. He will play a National Security Agency agent.