David Ridsdale told the Australian Royal Commission into Institutional Responses to Child Sexual Abuse that Cardinal George Pell tried to bribe him in a phone call in 1993, when he told him he had been abused.
He was abused by his uncle Gerald Ridsdale, who was previously convicted of more than 100 offences against children in the state of Victoria from the 1960s onwards.
According to The Guardian newspaper, Mr Ridsdale told the Royal Commission that Cardinal Pell told him over the phone: "I want to know what it will take to keep you quiet."
Mr Ridsdale declined and hung up the phone, before telling his sisters that Cardinal Pell "just tried to bribe me".
"I have never stated that Pell offered me anything specific or tangible in our conversation, only that his attempts to direct the conversation down a particular path made me extremely suspicious of his motivations and what he was insinuating," he added.
Cardinal George Pell has denied he said words of this effect on several occasions.
He was the auxiliary and Archbishop of Melbourne, which is located in Victoria, from 1987-1996, and the Archbishop of Sydney from 1996-2001. He was made the Vatican Secretariat of the Economy in February 2014.
Another abuse victim, Timothy Green, told the Royal Commission that he told Cardinal Pell he needed to stop another priest, Brother Edward Dowlan, from abusing boys.
When he did so, he said: "Father Pell said don't be ridiculous and walked off."
Several people have committed suicide because of the abuse which occurred in the Australian Catholic church.
The Royal Commission is awaiting a statement from Cardinal Pell regarding the accusations made against him within it.