The project has not gone to any council committee.
Waitemata Local Board chairman Shale Chambers said he had a heads-up on the project last month from the arts team.
"I was appalled at the proposal, which is a large-footprint, reduced-scale state house, with a chandelier within."
A spokeswoman for the housing lobby, Sue Henry, said that given Housing New Zealand was removing houses around the country it would be cheaper to uplift a state house and place it on Queens Wharf.
Barfoots managing director, Peter Thompson, would not comment about the sculpture or the cost.
"We haven't had any costings done ... We have had an anticipated amount, but that is confidential," said Mr Thompson, who does not expect the sculpture to be completed until January next year.
The artist, who created a series of stainless-steel bark poles inside the Britomart transport centre, could not be reached for comment.
Auckland Council manager of arts and culture Kaye Glamuzina said the project and gift to the city were perceived as regionally significant.
Waitemata councillor Mike Lee, who in his former role as Auckland Regional Council chairman secured Queens Wharf for public use, said he knew nothing about the sculpture.
Waterfront Auckland is also working on the project, but keeping quiet until a formal announcement.
In March last year, Barfoot & Thompson gifted $2 million to the city as part of its 90th anniversary celebrations.
The gift was made up of $1 million for the sculpture, $500,000 towards the upgrade of Holy Trinity Cathedral in Parnell and $500,000 to the Starship children's hospital.