Parts of Cardinal Connell's residence at Archbishop's House in Drumcondra and a section of Conliffe College look set to become protected structures despite objections from the Dublin Archdiocese.
Dublin City Council will debate on Monday a proposal from the assistant city manager, Mr Sean Carey, to make parts of both buildings protected structures. This means no alterations can be made to the buildings in future without special permission from the local authority.
The Dublin Archdiocese, which is headed up by Cardinal Connell, has objected to the move because it believes it is not necessary to add the buildings to the protected list.
The St Laurence O'Toole Trust, which owns the diocese's properties on behalf of the church, has objected to the plans. It claims the structures are already given sufficient protection and designating all of Clonliffe College is unnecessary.
However, the council is pressing ahead based on the belief that the buildings are of major significance.
Some parts of the Clonliffe building, which used to operate as a seminary, are prime examples of "ecclesiastical design", claims the council.
However, a consultant hired by the church authorities described them as "utilitarian in character".
Some of the objections from the Archdiocese have been accepted, but conditions have been laid down about any demolition or alteration to these parts in future.
In relation to Archbishop's House, the council is proposing to place a protection order on the stone wall running alongside the house. It also wants the milestone at the house protected.
The church authorities have told the council both these structures already have adequate protection, but the council has rejected this.
In total the following structures in the complex are being proposed for protection: the main college building, Holy Cross Church, the south link building, the ambulatory and the assembly hall (now used as a library), plus the two structures near the house.
Other parts of the complex at Drumcondra are already protected under the Planning and Development Act, 2000.
If the latest proposals are accepted at Monday night's council meeting it would make any major changes to the complex in future extremely difficult.
A spokesman for the Cardinal said the St Laurence O'Toole Trust was handling the matter and its views had been passed on to council officials in recent months.
The submission from the church authorities was made through Reid and Associates and historic building consultant Mr Robin Mandal was also involved.
The council states, in a report from Mr Carey, that it did not set out to give blanket protection to the whole of Clonliffe College.