However, that approach isn't supported by former Green MP Sue Bradford, who told the Herald that Green supporters shouldn't be in the dark on what Peters and his party were getting.
"In the end, the Greens couldn't go back to their people and make a decision without knowing what Labour had signed up to with Winston," Bradford said.
"You can understand why you don't know ahead of time. But at the point of being on the verge of signing, then all parties should know each other's position."
One of Labour's concerns is that the Green Party will put Peters off siding with Labour, either because of any objections to the Greens policies or because a three-party Government is more complicated.
Shaw told media yesterday that he trusts Ardern to arrive at a good deal for his party. That would be important in ensuring a stable Government that could pass legislation.
"Jacinda made fairness one of her principle values in the campaign. I have known her for a number of years and I said this before the election - I trust her, and she seems to be doing a good job of it."
Shaw would not say if the Greens were considering or open to the idea of sitting on the cross benches, instead of being part of a Government with Labour and NZ First.
The Greens are ready to conduct their special general meeting to get sign off at a moment's notice - and were prepared to hold the teleconference call as early as last night if necessary.
It needs 75 per cent support to go ahead - and the quick timeframe and confidentiality around discussions means the delegates responsible for signing off on the agreement will not get advance notice of the details.
Possibilities include full coalition with ministerial positions inside Cabinet, a support agreement with ministers outside Cabinet and a confidence and supply agreement from the cross benches. Shaw has favoured the full coalition model.
Labour will need the support of both NZ First and the Greens to form a Government. However, it is negotiating with both parties separately.
Green Party regional delegates will approve any deal involving the party, but that would be between only Labour and the Greens, with Labour signing its own agreement with NZ First.
The Greens have set up a reference group to link the negotiating team and the membership. It includes former co-leader Jeanette Fitzsimons and will decide how best to present the terms of any potential agreement to the party delegates.
That process is designed to counter the fact the delegates will not have much time to consider the agreement. The delegates would not have a chance to alter any of the terms during the meeting.
A membership vote would not necessarily take place. The party's constitution says a vote can be taken "if consensus on a motion is not achieved after reasonable attempts". This would happen if, for example, a party delegate blocked the motion.
Shaw said the Greens had campaigned hard to change the Government.
"That is what we campaigned on. We have thrown everything at it. That is what we are working on - securing that deal to change the Government."
NZ First has a strained history with the Greens, including when it vetoed the Greens from Government in 2005. Back then Peters made it a condition of his support for Labour that it was with the Labour Government only, not a Labour-Greens Government, on the grounds of stability.
The relationship has improved, but Peters has been highly critical of the Labour and Greens' memorandum of understanding, and yesterday told media the two parties had spent years "hugging", "embracing" and "loving" each other.
In July, Peters responded to then Green co-leader Metiria Turei calling him "racist" by saying such attacks would have consequences.
But yesterday he responded to questions about the Greens by pointing out he had never criticised the party's current leader, James Shaw.
"Contrary to what you people say, I've never had a bad word with him or about him, that you could possibly quote. Because I've never said something bad about him in my career," Peters said.
After the morning's meetings, Peters said the parties had talked only about policies - not ministerial positions - and he did not expect that to change. Asked if he'd want to be Finance Minister, he said "no."
"I said it's all about policy and it is. We've never mentioned anything about personal preferment and positions at all."
Bradford said that while Labour could sign separate agreements with the Greens and New Zealand First, Green supporters shouldn't be in the dark on what Peters and his party were getting.
She said there were areas where NZ First and Green policies overlapped where substantive gains could be made - such as regional development, transport and rail, foreign ownership, and opposition to the Trans-Pacific Partnership (TPP) trade agreement.
But there are stark policy differences. That includes on immigration.
New Zealand's population grew by 100,400 in the year to June. Net migration of 72,300 people contributed to this increase.
NZ First wants to slash net migration numbers to 10,000, while Labour says its own restrictions would cut numbers by 20,000 to 30,000 a year.
The Green Party had proposed capping migration at 1 per cent of population growth, but later abandoned that policy. Shaw had apologised for focusing on numbers, saying he was "mortified" at accusations by migrant groups that the Greens had pandered to anti-immigrant rhetoric.
Bradford said one area she has "nightmares" about, despite thinking it unlikely to happen, was if NZ First agreed with Labour to hold a referendum on the so-called anti-smacking legislation, which passed in 2007 after being introduced by Bradford, then a Green MP.
Peters said in a speech during the campaign his party's policy was to hold a referendum on the anti-smacking law.
"If I was in the Green Party and didn't know that was part of a deal [between Labour and NZ First], then you would be very angry. Whatever issue people are passionate about, people have a right to know," Bradford said.
"They should know, absolutely. It's only going to be an outline. It won't be every detail of policy."
Bradford said she saw merit in Labour negotiating separately with NZ First and the Greens. While she hadn't been a member of the party since 2009, she personally felt there was a mood to change the Government, even if that involved NZ First.
"I really hope that if this does happen, if they do make a deal, that they don't end up swallowing dead rats that are too big. I mean, that is always the question."