The building on the Castlewellan Road in Hilltown is currently vacant and is partially boarded up, having been damaged in an arson attack in 2023.
The building’s future has been uncertain since 2018, when Hilltown man Sean Faloon told the BBC that Fr Finegan had abused him on a regular basis from the age of 10 and that some of the sex assaults took place in the parochial house.
Several years prior to the 2023 arson attack, an anonymous threat was issued warning that it would be burned down.
'Time to reflect'
The current parish priest of Clonduff, Fr Charlie Byrne, revealed the demolition proposal during mass in St John the Evangelist Church Ballymaghery in Hilltown on Saturday evening.
"The last two years has given our parish finance committee and myself time to reflect and refocus our plans for parochial house, gardens and adjoining parish rooms," Fr Byrne said.
The parochial house sits on a plot of land between the church and St Patrick’s Primary School.
If the demolition plan is accepted, the land will be used as a car park drop off area for the school and a new purpose-built parish centre would be constructed closer to the church.
"We all have had a difficult journey deciding what is best here but we feel that this vision opens an exciting new chapter for the gardens of our school community and for our own parish community," Fr Byrne said.
Proposals will be brought to a meeting on 4 December where parishioners can have their say.
He added that the primary school had already reached capacity and needed more space, so it was hoped public support would be given to the car park plan.
Finegan was not mentioned as the finance committee’s proposals were read to the congregation.
The former Clonduff parish priest, who died in 2002, was also accused of sexually abusing boys at St Colman’s College in Newry, where he taught from 1967 to 1976 and rose to become its headmaster.
However, he was never prosecuted or questioned by police about claims made against him.
The Catholic Diocese of Dromore has already agreed large financial settlements with some of Finegan’s victims.