Former Green Party MP Keith Locke says his contemporaries should stay out of Cabinet in order to remain critical of Labour while also working constructively with it.
Any Cabinet positions offered to the Greens by Labour would be a favour, not a necessity, and likely require the smaller party to soften its criticism.
The two parties are meeting again today to thrash out areas they can co-operate on in government.
With Labour holding an election night majority, the Greens aren't needed in a formal coalition arrangement.
The parties met twice last week in the prime minister's office and will do so again later today, with Jacinda Ardern expecting to complete talks this week.
Locke told Morning Report: "I think the Greens have to recognise that people voted for them because they like the Green vision and policies but also where possible to advance the progressive agenda with Labour.
"I think the best way forward on that... what we need really is a co-operation agreement whereby the Labour and the Greens work together to progress certain agreed issues and bills.
"The agreement could provide for easy Green access to Labour ministers, harmonious working relationships between the two parties on select committees, etc."
He thought the Greens should avoid Cabinet positions if possible.
"Because Labour has a complete majority, they would be granted as a favour not a necessity. The Green Party would not have any leverage and there would be an implicit understanding that the Green caucus would soften its criticism of the Labour government."
The Greens should push for change using the Parliamentary positions they already have, he said.
"Take for example Ricardo Menendez-March fresh from Auckland Action Against Poverty. I think he could really provoke more change in the welfare area by speaking out, linking up with the lobby unions, using Parliament as a platform, and linking up with the [welfare] minister.
"If it is Carmel Sepuloni, in the past [she] hasn't been able to achieve much change because she hasn't been given the budget ... but pressure from the Green Party inside and outside Parliament might have an effect.
"The Greens have produced many changes over the years."
But he said it was a "completely new situation now" with a confidence and supply agreement "completely irrelevant".
"The Greens in any case should reserve the right to abstain or vote against the budget...
"Change can be made and it's important that the Greens be an independent and critical voice working co-operatively and challenging from outside the Cabinet."