Travolta plays John Gotti, the leader of the legendary Gambino crime family.
A spokesman for the film said the film is being shot on a budget of $75 million, but no more details would be released until April 12.
A person with knowledge of the film said the movie will be directed by Nick Cassavetes and produced by Marc Fiore.
The famous mobster died in prison in 2002. Gotti's son, John "Junior" Gotti, sold film rights to Fiore in 2010 for an undisclosed amount.
The Associated Press contributed to this report.