Architect Julia Gatley, an authority on modern architecture in New Zealand, has praised it as a beautifully proportioned, slender building that encapsulates modernism.
It has no heritage status, but two reports have suggested it warrants a category A listing, and the council's heritage division says it merits category B status.
JLL (Jones Lang LaSalle) research director Justin Keane said the building could become a B grade office building, but it also "screams apartment conversion".
He said it would cost between $5 million to $10 million to remove the remaining asbestos in the building. In 1989, 350 tonnes of asbestos were removed.
Mr Keane put asbestos removal and refurbishment costs for the 14,300sq m building at $34 million to $53 million.
At the time of the ASB deal in 2011, the council estimated the cost of refurbishment at $93 million. In April this year, it priced a retrofit at $70 million.
The head of the council's property arm, David Rankin, said a report had been received from JLL on investor interest in the building, but that was only part of the picture.
"There is a trade-off around the cost of refurbishment of the building, the use you make of it, whether that stacks up financially, how that relates to the heritage features. It's far from straightforward," he said.
The administration building could be used to house 200 to 300 staff from the council's regional facilities arm, who are now located in the Aotea Centre.
That would create administration and rehearsal space for the Auckland Philharmonic Orchestra and the Royal NZ Ballet.
