Prime Minister John Key is to sound out the Greens about a closer more formal relationship - possibly involving the Greens abstaining on confidence and supply.
He's due to meet with co-leaders Russel Norman and Metiria Turei this afternoon.
However Ms Turei says like confidence and supply, abstention remains a "highly unlikely" prospect.
"In the first instance I want to have a discussion with them about what the future of the two parties is," Mr Key said.
"If there is no future, then its basically a policy-type agreement ... If there's a broader relationship to be had, then I'm interested in having those discussions."
Mr Key confirmed he would be raise the prospect of the Greens abstaining on confidence and supply during this afternoon's talks, saying there "might be conditions under which they would, but I just want to test that out".
The two parties had a memorandum of understanding (MOU) during the last term, which included home insulation, pest control, and toxic site clean-up programmes.
In the months before the election, the Greens softened their previous position that they could not provide confidence and supply to a National led Government by saying it was a possibility but a highly unlikely one.
However Mrs Turei this morning said the Greens regarded abstention as close to a confidence and supply vote.
"Therefore again it would be highly unlikely."
"We are going into these discussions we want to talk with them about an extended MOU, we're open to hearing what they've got to say and we'll see what happens once we've had those talks."
Despite a closer relationship remaining an unlikely prospect, the Greens hadn't closed the door on the prospect.
"We are open to hearing what they've got to say and what they want to put on the table - until we see and hear what they've got to say it's very hard to know what our position is."
If Mr Key was to seek a closer relationship, the Greens would look for major policy gains and Dr Norman said those were likely to be the Green's priority areas of reducing child poverty, cleaning up waterways and creating "green" jobs.
"Welfare reform, stopping the sale of state owned assets, and stopping deep seal oil drilling were also issues we raised during the election and if he wants to talk about those we're open to having that conversation," Mrs Turei added.