Stone will direct the picture from a screenplay by his "Wall Street" co-writer Stanley Weiser.
Shooting is expected to start in Shreveport, La., at the end of next month, the entertainment industry trade paper said.
Cromwell's film credits include "Becoming Jane," "The Queen," "The Green Mile," "LA Confidential" and "Babe."
Burstyn has starred in "The Exorcist," "The Last Picture Show," "Requiem for a Dream" and "Divine Secrets of the Ya-Ya Sisterhood."
Justin Bieber crashes Drake Bell's album release party
Members of Congress to keep receiving porn magazine