At the moment the city-based staff are in nine buildings around the city, including the Civic Building in Aotea Square, which has been the headquarters of the former Auckland City Council since it opened in 1966.
However, the 19-storey building, once the tallest in the city, is riddled with asbestos and cannot be altered without huge disruption at major cost.
Mr McKay yesterday said he was limited in what he could say because the council was in negotiations.
But he confirmed the council had been looking at five options in the city, ranging from leasing to constructing a new building.
A confidential report on the matter to be discussed at today's strategy and finance committee meeting is understood to recommend going with the ASB Tower.
Asked about the tower, Mr McKay said: "We know it is going to be vacated over the next two to three years and it is reasonably well located."
Cost savings from consolidating city staff into a single building is understood to be a big factor in the decision to move.
"It is all about starting to realise the transformation of benefits of being the new Auckland Super City," Mr McKay said.
"We have got to now behave and react in different ways that were never possible before."
Mayor Len Brown and his office have no plans to move from the Auckland Town Hall, a short walk from the Civic Building and the ASB Tower.