Investigators are trying to find the drug dealer who supplied the actor with the heroin while also determining if Hoffman had prescriptions for the many anti-anxiety drugs, muscle relaxers and attention-deficit disorder pills found in his Manhattan home, the Post said.
The New York medical examiner's office told CNN it began an autopsy Monday to determine the cause of Hoffman's death.
The Oscar winner's body was found on the bathroom floor of his apartment Sunday morning. He was 46.
Police said they suspect he died of a heroin overdose because a needle was found in his arm and drugs were discovered in his home.
The star of "The Master," "Capote" and "Twister" had spoken candidly about a history of substance abuse which dated back to his 20s. He reportedly had been clean for more than two decades when he suffered a relapse in 2012 and started using drugs again.
The exact cause of death likely was unlikely to be determined for several weeks pending results of toxicology tests, the medical examiner's office said.
At the time of his death, Hoffman was working on a new Showtime comedy series called "Happyish" but the fate of the project is now unclear.
"Philip Seymour Hoffman was one of our generation's finest and most brilliant actors," the cable television network said in a statement. "He was also a gifted comedic talent. It was a great privilege and pleasure to work with him and we are all absolutely devastated by this sudden loss. Our thoughts go out to his family at this very difficult time."
"We are heartbroken by the loss of our beloved friend, company member, and former artistic director, Philip Seymour Hoffman," New York's Labyrinth Theater Company said in a statement. "His contributions to the Labyrinth family as an artist and mentor are immeasurable. We join everyone in mourning the passing of one of the great lights of our generation."
Hoffman also played the supporting role of Plutarch Heavensbee in "The Hunger Games" film franchise. The blockbusters' Lionsgate studio described the actor in a statement as "a singular talent and one of the most gifted actors of our generation."
"We're very fortunate that he graced our 'Hunger Games' family. Losing him in his prime is a tragedy, and we send our deepest condolences to Philip's family," Lionsgate said.
"Words cannot convey the devastating loss we are all feeling right now," said a separate joint statement from "Hunger Games: Catching Fire" and "Hunger Games: Mockingjay" director Francis Lawrence and the books' author Suzanne Collins. "Philip was a wonderful person and an exceptional talent, and our hearts are breaking. Our deepest condolences go out to his family."
Hoffman is survived by his three young children and longtime partner Mimi O'Donnell.