But the Auckland Council and Auckland business community supported it. "I think we would make a very strong bid for it."
A secretariat, however, would have to be independent of the host Government.
Other countries thought to be interested in hosting a secretariat include Singapore, where former Reserve Bank Governor Alan Bollard heads up the Apec secretariat.
Chief Trans-Pacific Partnership negotiators, led by New Zealand's David Walker, will be meeting in Auckland this morning.
Top of their agenda will be what happens to prospective new members over the next two years, before the deal is able to come into force.
Indonesia, South Korea, Thailand and Columbia are among those countries that have expressed some interest in joining.
"There will be countries that are very keen," Mr McClay said. "In some cases we will want them to do various things to get ready and in other cases we will need to give them a pretty clear steer.
"It's 40 per cent of the world's GDP at $27 trillion worth of TPP spend.
"There are a lot of countries who are thinking it would be madness not to be involved."
Mr McClay said if a small secretariat were established, it could do more work for ministers on the issue of accession to the TPP.
In his view, countries would have to be willing to sign up to what was already agreed. There would be no reopening of talks, except on tariffs.
United States Trade Representative (minister) Mike Froman, who chaired the TPP talks, is expected to report to other ministers on the prospects of the deal being passed by the Congress before the summer break in July.
A suggestion by visiting US TPP critic Lori Wallach that the US would try to reopen talks on the patent period for biologic drugs was dismissed in terms of New Zealand.
Mr Key said last night that there would be no change to the five years New Zealand negotiated.