The New York Police Department is investigating, and the Office of the Chief Medical Examiner is working to determine the exact cause of death, the Journal says.
The paper quotes an un-named law-enforcement official who says Mr Hoffman was found dead at his apartment in the West Village neighborhood of Manhattan.
The actor was found in the bathroom of his fourth floor apartment in the Pickwick House around 11:15 a.m. by a screenwriter, who called 911, the official said.
Mr. Hoffman won the Academy Award for Best Actor for the 2005 film, "Capote." His other films include "Boogie Nights," "The Big Lebowski", "Magnolia" and the "Hunger Games" franchise.
The latest installment of the "Hunger Games" series is in post-production.