It is understood progress on the 620,000 sq km ocean sanctuary around the Kermadec Islands has been considered as part of the Greens' deal with Labour should NZ First opt for Labour to form the next government after last month's inconclusive election result.
It is the first policy detail to be leaked from the talks, which have been held under strict confidentiality.
Green leader James Shaw refused to confirm or deny the Kermadecs was in the Green Party deal.
"I have no comment on any of the negotiations and neither have I had any comment on the content of the negotiations at any point."
In the past both Labour and the Green supported the sanctuary, which would be the biggest in New Zealand waters. It was part of Labour's policy in 2014.
However, Labour put its support under review after Te Ohu Kaimoana - the Maori Fisheries Commission - mounted a legal challenge to the sanctuary in the High Court, arguing the legislation stripped fishing quota without consultation or compensation. That legal action is still under way.
Labour's support is likely to be conditional on the outcome of that.
Although the Green Party had always argued the sanctuary should go ahead regardless of the Maori rights, it would cause ructions in Labour's Maori caucus unless Labour worked out a way to resolve Maori concerns or agreed to wait for it to be tested in the courts.
Legislating to override Maori rights or prevent Maori testing those rights in the courts would create a similar controversy to the Foreshore and Seabed Act - and Labour will be wary of that.
All government negotiating talks have been held in strict confidence so while Labour's deputy leader Kelvin Davis will know of the proposal, the Maori caucus has not yet been briefed.
The Green Party's deal is almost complete and the 170 or so delegates are ready to vote on it by a teleconference which could happen tonight , in advance of NZ First's board meeting to decide between the Labour and National packages on Monday.
It is understood NZ First has made it clear it wants the Green Party to sign off on its deal before NZ First makes its choice so it can be sure Labour has the numbers to form a government.
In 1996 - the last time NZ First was in this position - NZ First went with National partly because Labour could not guarantee the Alliance Party would provide confidence and supply.
On Saturday Mr Peters was keeping his counsel, refusing to even reveal where he was but said work was ongoing throughout the weekend as NZ First checked details such as policy costings with National and Labour.
National leader Bill English was in Wellington but also keeping quiet while Labour leader Jacinda Ardern was in Auckland at the Diwali festival.
Any attempt to forge ahead with the sanctuary without resolving the Maori fisheries issue will also likely be objected to by NZ First.
NZ First MP Shane Jones was one of the architects of the Maori fisheries settlement, known as the Sealords deal, and while Mr Peters had not supported that settlement, he had pulled his support for the sanctuary because he believed it breached the settlement legislation.
TIMELINE
29 September 2015: Then Prime Minister John Key announces 620,000 sq km Kermadec Ocean Sanctuary at the UN General Assembly in New York - the highest category of protection and all fishing and mining would be banned.
8 March 2016: Legislation to create the sanctuary is introduced.
15 March 2016: Bill passes first reading with unanimous support.
20 March 2016: Te Ohu Kaimoana (Maori Fisheries Commission) lodge claim in High Court to try to stop the sanctuary.
12-13 April 2016: The Maori Party and Labour put support under review after the legal challenge by Te Ohu Kaimoana. Act and NZ First pull support.
23 July 2016: Select Committee recommends sanctuary go ahead with a review after 25 years to assess the fishing rights issue.
14 September 2016: Talks between Government and Te Ohu Kaimoana fail. Maori Party raises prospect of walking out on National if sanctuary goes ahead.
20 September 2016: Prime Minister John Key puts the sanctuary on hold saying he will not proceed until the issue is resolved with the Maori Party.
- By Clare Trevett