However, this might change soon, as the actor is in talks with Clint Eastwood to play J Edgar Hoover in a new movie biopic.
Speaking to E Online, the actor explained that the founding director of the FBI was involved in some of America's most scandalous events, from Vietnam to the assassination of Martin Luther King.
However, he didn't mention that Hoover was reportedly a cross-dresser in his spare time.
When quizzed as to whether he would be donning sexy fancy dress and going in drag for the role, Leo was coy.
"We haven't done the fittings for those," he quipped.
Given the actor's baby-faced features, we could see him in something like an Ann Darrow fancy dress costume from King Kong, or perhaps as a Daphne from Scooby Doo - what do you think?