However, work continues on a detailed assessment, and options regarding seismic strengthening are expected to be put in front of councillors early next year.
Substantial restoration is also required of the exterior facade and work on this is expected to be carried out until at least 2028.
The Dunedin Centre in the Octagon is made up of the Municipal Chambers, Town Hall and Glenroy Auditorium, built between 1880 and 1930.
Some ornamental Oamaru stone fell from the chambers building in 2020, leading to precautionary measures being taken around it and the Town Hall, as both were due for remedial work.
Detailed investigations began the following year and in 2022 Dunedin City Council meetings were shifted out of the Municipal Chambers and have yet to return there.
The council did not include funding for strengthening the buildings when it adopted its 2025-34 long-term plan last month, but $14million was allocated for heritage exterior restoration, seismic investigation and some other work.
An update about the programme is set to be discussed by the council this week.
A report for councillors said the centre’s interior had been modified over the years and some structural work had been carried out.
The centre’s seismic resilience was "not well understood" and some interior fixtures and mechanical systems were "either in poor condition or approaching the end of their serviceable life".
"Over time, parts of the exterior facade have been renewed. However, the exterior is now at a stage where a more wholesale restoration is required."
Scaffold gantries were put up after the October 2020 incident to prevent harm to pedestrians by catching any more material that might fall.
The council said there had since been "further occasions where stone, slate and cast-iron balustrades have fallen from the building".
Seismic investigation and exterior restoration were regarded as separate, but connected, projects.
Engineering consultants WSP was engaged this year to develop a detailed seismic assessment of the property.
It is expected to be completed and reviewed by the end of this year and council staff said they intended to produce a report for councillors about options for strengthening, including potential costs, early next year.
Regarding the exterior, the council said a sealant was historically applied to the Oamaru stone surface.
"While this approach was a common practice for the time, the types of sealants used did not allow the stone to breathe."
Moisture could be trapped under the sealed layer, dissolving the stone over time.
