Director Phillip Noyce has revealed he would like to make a film about the whistleblower, who is charged with violating espionage laws, and wants the Hunger Games star in the lead role.
He told NBC News: "He's perfectly positioned as a rising star. I think he'll probably be one of the great ones. His older brother, Chris, could also play him but Liam looks more like an everyman. I think he'd be perfect."
The filmmaker said he has been fascinated by the story of Snowden, who is currently in Moscow and has been on the run since exposing US authorities' data-gathering PRISM programme.
He said: "This is a movie that's playing out before our eyes, even though we can't see anything. We can't see the hero or the villain - the central character.
"Like my last big movie, Salt, it's a story where you're not quite certain if you're dealing with a heroine or a villain. And we may not be certain until the end of the movie or even beyond that. That's a beautiful duality to deal with when you're making a story or watching a movie. You can speculate he's motivated by complete unselfish motives through belief in protecting worldwide public interests. Or you can speculate he was himself a victim of knowing that notoriety might bring him immortality."
Liam, who is engaged to singer Miley Cyrus, can be seen in the second Hunger Games film, Catching Fire, later this year.