The 'Batman Forever' star has been staging his play Citizen Twain in various venues across the US for over a year, and he is due to take the production to London's West End this autumn.
However, there is still one big stage Kilmer is keen to set foot on as the legendary storyteller, reported Daily Star.
Kilmer was asked about the possibility of staging the play on Broadway during an appearance on the New York-based Late Night with Jimmy Fallon.
He said, "I've been meeting producers here. I'll do it here."
The actor's play is part of his research for a planned movie he's writing about Mark Twain and his relationship with religious leader Mary Baker Eddy.