Part of that will include what new provisions should apply for the deal to enter into force.
Under the old deal, it included a GDP trigger which effectively meant that both the United States and Japan had to ratify it in order for it to take effect.
With President Donald Trump having withdrawn the US from the deal in January, the entry-into-force provision has to be changed.
Parker would not comment on whether that should be a simple majority of TPP11 countries or whether it must also include Japan - which has taken over leadership of TPP since the US withdrawal.
"We must find a solution to allow us to ban overseas buyers of existing New Zealand homes for us to proceed with TPP11," Parker said. "We are open-minded as to where that solution sits, whether it sits within TPP or outside of TPP."
He would not elaborate on what that meant. But it is possible that the ban - which is due to passed as a priority policy in the Government's first 100 days - could be specifically mentioned in the new domestic legislation needed to change the entry-into-force provisions.
Asked if he thought New Zealand would be protected from claims of a breach of TPP if the ban was passed before TPP's entry into force, Parker said: "We are considering that very issue. There may be differences in what you do before and after it comes into force."
Parker said New Zealand officials in Tokyo were also raising the issue of the Government's opposition to Investor-State Dispute Settlement [ISDS] clauses, although his language around expectations of success on that issue was soft.
"We don't want the ISD provisions applying to us and so we will be instructing our negotiators to use their best endeavours to fix that."
It is clear that the issue on which there will be no compromise is the ban on house sales.
"I want to leave Apec assured that we are not trading away the right of New Zealanders to ban foreign buyers of our homes."
And a completed TPP11?
"There are undoubted trade benefits in TPP11. They are obviously not nearly as significant as they were when the US was part of the deal but nonetheless a residue is still important, particularly into Japan.
"But if I was forced to trade between the principle of protecting New Zealanders' rights to have control over who owns our houses and TPP, which I hope we will not be forced to choose between, then our promise in respect of who buys New Zealand homes will prevail," he said.
"I am reasonably confident that we can avoid that binary choice."
Asked if he was ruling out the use of stamp duty, he said: "Correct."
It was not an uncomplicated solution and he had been advised it could cut across provisions of previous trade agreements.
Parker still harbours strong resentment that the previous government did not make provision for a potential Labour government policy.
"It has absolutely been clear for many, many years that the Labour Party in terms of trying to maintain bipartisan consensus around this has been strong on this ability to have New Zealand markets for our land, not international markets, and therefore how the last government chose to do that was an attempt to wedge us," Parker said.
"We believe we've got a strong record on trade - Mike Moore, WTO head, China Free Trade Agreement, various other free trade agreements, we've been an outwardly looking trading nation under every Labour government, going way back when.
"They were trying to besmirch that reputation by forcing us to trade between that and our principles, belief that our land assets ought to be priced according to the means of New Zealanders and the New Zealand market, not an international market."
Asked if Groser, a former trade diplomat before entering politics, would continue to be of benefit in Washington, Parker deferred to Peters, but then said: "He is one of the people who wedged us on this issue."
Groser, when Minister of Trade, negotiated TPP and the South Korean free trade agreement, and he knew Labour's concerns about the limits of sovereignty of a future government.
"He was pretty central to those decisions."
The house-ban issue is likely to come up at the first business meeting of the new Government tomorrow when it finalises its 100-day programme.