The First World War memorial, on the St Mary the Virgin church grounds in Hunslet, has remained outside the church since it legally closed in April.
Resident Peter Blower and his wife Hazel, who grew up in Hunslet and now live in Belle Isle, found the lesser-known monument, a cross and marble stones bearing dozens of names, after carrying out their own research.
They uncovered that Mrs Blower’s great uncle, Oscar Stocks, who served with the West Yorkshire Prince of Wales regiment in the Great War in 1918, is commemorated on the memorial.
Now, ahead of the centenary marking the end of the devastating conflict, they are asking for the monument to be moved to a more prominent location, so they can remember the young men from Hunslet who sacrificed their lives.
Mr Blower, 67, said: “Hunslet was one of the biggest contributors of young men in Leeds during the war.
“The way it is, it's inaccessible and you can’t see it from the main road. It’s at the side in a little alcove and the church is closed now.
“A lot of people from Hunslet just aren’t aware of it.
"We want the memorial to be moved somewhere that we can remember these lads."
The church legally closed to the public on April 30 this year, and its services have been consolidated as the Parish of Hunslet and Belle Isle.
Father Chris Buckley, Vicar of the parish, said the church was in “ongoing discussions” about the memorial.
However, once legally closed, he said ownership of church buildings are then passed on from parishes to the Leeds Diocesan Board of Finance.
But the church grounds remain the responsibility of the parish.
The parish is bound by strict permission when it comes to moving items on Church of England grounds, he said.
Father Buckley said: “If anything has to be moved there is a complex system called a Faculty Law in the Church of England to move any items.
"We would certainly support that but it would take a long time to sort out.
"We certainly share the concerns and we fully understand."
Father Buckley said a service will still be held at the memorial, in the church grounds in Church Street, on Remembrance Sunday from 1pm.
He said fencing surrounding the memorial, which believes was erected initially to protect it from building work at the nearby school, will remain.