The production attracted attention earlier this week when LaBeouf, 21, was arrested for allegedly trespassing at a Chicago Walgreens just days before the film was slated to start shooting in the Windy City.
Directed by "Taking Lives" and "Disturbia" director D.J. Caruso, "Eagle Eye" is about two people framed as terrorists and forced to join a group plotting a political assassination, the Hollywood Reporter said.
Thornton, who has starred in "Mr. Woodcock," "Bad Santa," "Sling Blade" and "Pushing Tin," will play a hero in the new film, the trade paper said.
Notable deaths of 2014 [PHOTOS]