The Green Party has made another approach to National about working more closely on specific issues.
Mr Key rebuffed an approach during the campaign for a possible working relationship after the election.
But Green Party co-leader Metiria Turei said New Zealand had benefited when the two parties had co-operated, including over the national cycleway and home insulation.
"I think we should consider that again. I've written to John Key to see if they are interested in that and I hope that he responds positively, because I think New Zealanders will benefit from Greens and National finding common policy ground and working together," Ms Turei said.
The Greens had been able to work with National on specific projects in the past while still disagreeing with much of their policy, she said.
Mr Key said he would consider the proposal but doubted the two parties would settle on any kind of formal relationship.
"We'll take the letter. We'll give it some consideration. We did work with them on a number of issues," he said.
"Whether we'd have a formal memorandum of understanding is something I'll take back to my colleagues but to really want to go to that step, we'd have to believe there was something a bit further down the track, and historically the Greens have really just said that they don't want a bar of a National-led Government."