The football star, who has been sectioned, made the dramatic statement as he recovered in a police station after a night out drinking.
Venables, who managed Gascoigne when he played for England and Tottenham Hotspur, said he had no doubt Gascoigne meant it and that without treatment the former player was in serious danger of killing himself or somebody else.
"But something had to be done because I've seen first-hand just how bad Gazza is – and I can't stand by and let it run and run until we all end up at his funeral."
Venables said he realised the depths of despair that Gascoigne had reached when he was called by police to a station in Kensington, west London.
Gascoigne had been pulled in by police for his own safety after he was behaving in a disturbed manner after a night out drinking.
He found the former Tottenham, Lazio and Newcastle player slumped in a corner, smoking a cigarette.
At first there was no response from the troubled star but eventually he came around and the pair chatted about past footballing glories.
It was then that Gascoigne made his admission.
Venables said: "The conversation had brought him round and, surprisingly, he asked the policeman in the room to leave us alone for a second.
"As the door closed, Gazza looked straight back at me. I felt he was sober at that moment. His stare was quite chilling really and that's when he frightened the life out of me. He simply said: "I want to kill myself".
"It was an awful moment and I have no doubt he knew what he was saying. Had he kept drinking like he was, he was going to die.
"Whether his body packed in on him, like George Best, or he darted in front of a car oblivious to where he was, I don't know. But it was going to happen."
Venables was speaking out just a day after Gascoigne was sectioned for three months.
Gascoigne, 42, was taken to a hospital, which has not been named, under the Mental Health Act.
He is thought to have agreed to the drastic action after repeated pleas by friends and family to tackle his problems.
Gascoigne is thought to have experienced manic depression, paranoia, bulimia, obsessive compulsive disorder, attention deficit disorder, and a mild form of Tourette's Syndrome.
I really hope he can get well.