US Edition The 36 year-old was an aspiring film-maker who also acted in two movies with his father in the 1990s, including his debut as the son of boxer Rocky Balboa in Rocky 5.
The celebrity website tmz.com and the New York Post reported that he was believed to have died after an overdose of pills.
Citing unnamed sources, the newspaper said that pills were found at his home, but it was unclear if his death was a suicide or accidental.
The Los Angeles police department has referred the case to the city coroner's office. Police sad there was no suspicion of criminal activity or foul play.
His father returned to Los Angeles from San Diego, where he had been attending the Comic Con convention to promote his new film The Expendables 2 with with Arnold Schwarzenegger and Dolph Lundgren.
"Sylvester Stallone is devastated and grief-stricken over the sudden loss of his son Sage Stallone," said a representative for the star. "His compassion and thoughts are with Sage's mother, Sasha. Sage was a very talented and wonderful young man. His loss will be felt for ever."
George Braunstein, the dead man's lawyer, said: "It's a tragedy. He was a young, talented extremely good filmmaker and a lovely person.
"We don't know any of the details but it must have been some sort of tragic accident. He was full of life and working on projects," Mr Braunstein said. "He wasn't at all depressed or anything like that."