Fr Paul Moore, from Ayrshire, Scotland, said the money to the altar boy was a "loan" and a "private matter".
The Catholic priest had admitted to child sex offences to the then Bishop of Galloway, Maurice Taylor, in the late 90s but he escaped police prosecution.
A BBC investigation found one of the alleged victims, an un-named man now in his 40s, claims to have been abused for several years as a teenager in Ayrshire.
A cheque for £10,000, seen by the BBC, is made out to the man from Fr Moore, 79, in 2009.
The alleged victim said it was "more than conceivable" the money was intended to "keep him sweet" but he added he did not threaten to go to the police if the money was not paid.
When confronted by the BBC Fr Moore denied that he had ever admitted to child abuse, however Maurice Taylor has said this took place.
Mr Moore said the cheque was a loan: "I lent him that because I wasn't using it - it was sitting aside and when I'm asked to help people that's what I try to do."
He accepted that the money could look like "hush money" because an allegation had been made against him by the man.
"Sure, it looks now, I realise that now in these times but it's not that, it wasn't hush money.
"In the Bible it says lend without hope of getting things back... as far as I'm concerned he can keep it."
He said the Church was aware of the money he gave but the Catholic Church has not been available for comment.
The BBC reported an alleged victim of the priest had made a claim to Police Scotland saying he was abused at St Mark's Primary school in Irvine, Ayrshire, where Fr Moore was chaplain.
A police spokesman said: "We can confirm that Police Scotland has received a report of historical sexual abuse and our inquiries are ongoing."
