"This came completely out of the blue," the source says. "Sylvester did not see this coming for one minute.
"Sage was healthy, and Sylvester thought he was doing really well, this came from complete left field.
"Sylvester was very close to Sage and he is absolutely overwhelmed with grief by his death. He is totally stunned and still in a state of shock."
As RadarOnline.com previously reported, Sage, was found dead from a suspected drugs overdose Friday.
Sage, full name, Sage Moonblood Stallone, was 36 years old.
He was Sylvester's son from his first marriage to Sasha Czack.
An actor, director and producer, Sage appeared in the fifth installment of Sly's biggest film franchise, Rocky, where he played the title character's on-screen son, Robert Balboa.
Most recently, Sage appeared in a 2010 movie called Promises Written In Water and a short titled The Agent.
His short-lived marriage to Starlin Wright in May 2007 was annulled after just 10 months.
Stallone's rep, Michelle Bega, released a statement Friday afternoon: "Sylvester Stallone is devastated and grief-stricken over the sudden loss of his son Sage Stallone. His compassion and thoughts are with Sage's mother, Sasha. Sage was a very talented and wonderful young man. His loss will be felt forever."