All those agencies were involved in urban development, he said.
"If we need a fifth, we need to ask what went wrong with these four."
Asked whose fault the Auckland housing crisis was, Kimpton refused to blame anyone.
"I won't point the finger. The issue is not land supply, the issue is not the ability to manage construction to get things built."
Home builders and contractors had a role to play and so did apprenticeship schemes, he said.
Deputy mayor Penny Hulse this week in a Herald opinion piece wrote she was deeply concerned about whether the construction industry had the capacity to build the houses needed fast enough. "A government housing building programme may have to form part of the solution," Hulse wrote.
Kimpton said Auckland needed at least 13,000 new residences annually yet only about 9000 were being consented and from that, only about 6000 were being built.
But even those numbers were a big increase on the 3000 to 4000 residences being built only recently.
Asked if he or any other council official had known about Key's plans, Kimpton said: "I'm not aware of that."
Asked if he was talking directly to ministers about the new authority, he referred only broadly to ongoing discussions between the Crown and council over various issues, including roading and developments in Manukau and Northcote.
However, Kimpton did acknowledge the council could have acted differently in hindsight.
Panuku and the development programme office could have been formed sooner, and the council could have lobbied the Government harder about funding of infrastructure, Kimpton said.
Property Institute of New Zealand chief executive Ashley Church urged the Government to exercise caution before setting up the authority.
"Isn't this why the Super City was set up?" Church said.
"If the creation of a single authority was the answer to the housing problem, Auckland would now be well on the way to solving its housing issues."