President Donald Trump made an overt play at the weekend for the United States to rejoin the TPP a week after a revised deal without the US was concluded.
But New Zealand Trade Minister David Parker says the US has weakened its negotiating position.
Australian Deputy Prime Minister Barnaby Joyce, however, has raised the prospect of late changes being made to bring the US aboard, despite it being set down for signing next month.
Trump's speech at the World Economic Forum in Davos, Switzerland, was more conciliatory towards TPP compared with his campaign claims it was a disaster and withdrawing the US as soon as he took office.
He talked about bilateral deals with individual countries but said the US could negotiate with the group if it was in everyone's interests.
"The United States is prepared to negotiate mutually beneficial, bilateral trade agreements with all countries," Trump said at the weekend. "This will include the countries within TPP, which are very important."
The US already had agreements with several of them - Australia, Canada, Chile, Mexico, Peru, Singapore.
"We would consider negotiating with the rest either individually or perhaps as a group if it is in the interests of all."
About 20 provisions of the TPP which the United States negotiated when it was a member of TPP have since been suspended, such as keeping copyright at 50 years and not 70, and requiring greater transparency around Pharmac's decision-making.
And some new provisions have been negotiated among the remaining 11, such as narrowing the ability of foreign investors to sue Governments.
David Parker, who was at Davos, agreed that the suspension of US-driven parts of the deal could well have contributed to making the deal more attractive to progressive Governments.
"Their negotiating position is of course weakened by the fact that they are no longer in TPP."
Asked to comment on Trump's comments that he would consider rejoining TPP if the deal was improved, Parker quipped: "If he means much improved, like improved access for dairy products into countries of the world and he wanted that and it could be achieved through TPP, we'd love that."
But he said the US's real concerns were around the subsidies that some countries paid their exporters – which did not include New Zealand, Australia or Japan.
Trade officials concluded a new TPP deal without the US in Japan last week and ministers are due to sign it in Chile on March 8.
Barnaby Joyce, speaking on Sky TV, said that because the deal had not been signed, he did not want to say positions were finalised.
"The final draft of it, I hope, is determined once the United States is part of it."
Parker took part in a discussion at Davos on how to improve the reputation of trade.
"I said speaking for ourselves and I suspect other western countries, it is unsurprising that some people are suspicious of trade when they think that too many of the benefits accrue to multinational companies that don't pay tax anywhere.
"On the positive side, I said that frustrating though the WTO and trade agreements are, they are necessary to have an international rule-of-law in trade around things like illegal fishing, and subsidies for fishing and subsidies for fossil fuels."