The decision prompted LaBeouf to drop out of the running for The Bourne Legacy, a role which has since gone to Jeremy Renner, while the star also quit talks for the upcoming Rise of the Planet of the Apes.
He was also approached to take on leading roles in Oscar-nominated films 127 Hours and The Social Network, but while LaBeouf enjoyed the finished movies, he turned down the jobs because he wasn't convinced they were "game changers".
And the star is adamant he will continue rejecting major projects until he finds one which allows him to emulate his Hollywood icon.
In a new interview with Details magazine, he says, "I am trying to impress myself. I have yet to do it. I'm looking for Warren Beatty-type game changers."
LaBeouf is also a major part of the ongoing Indiana Jones film franchise after playing the adventurer's son in 2008's Indiana Jones & The Kingdom of the Crystal Skull.