Cathedral administrator Monsignor Bernard Kiely said the first stage of the project was the restoration of the cathedral, completed in 2007.
The council is now considering other surrounding buildings.
A council statement said: "Future developments around the square include the likely extension to Liston House and the conservation and the renovation of the presbytery.
"The council has an agreement with the Roman Catholic Bishop of the Diocese of Auckland to swap the public land required for these developments with other land ... which is to be used for public open space.
"We will continue to work with the diocese on this project."