Incoming Prime Minister John Key has indicated that one option he discussed with the Maori Party on Tuesday is the possibility of a ministerial role outside Cabinet.
Mr Key and Maori Party co-leaders Tariana Turia and Pita Sharples described the meeting at Parliament as 'constructive', as talks to form a National-led government continued for a second day.
The leaders of ACT and United Future appear set to receive a ministerial role outside Cabinet in return for pledging support on confidence and supply.
Mr Key indicated a similar arrangement is under discussion which may see the Maori Party with a position of minister outside Cabinet, in return for abstaining, or supporting National on confidence and supply.
The incoming Prime Minister was asked after the meeting about any discussions on ministerial roles.
"Look, those options are potentially on the table," he said. "There's a consistency of view that we're taking across all three parties that we're talking to, but I don't want to detail those at this point."
Mr Key is hoping to announce his new Cabinet line-up by Sunday, and to be sworn in as Prime Minister early next week, in time for him to attend the APEC meeting in Peru on 19 and 20 November.
He will receive a briefing from Treasury officials on Wednesday about the state of the Government's books.
The Maori Party will consult its supporters about the options on the table, and is leaders expect that could be completed by Sunday.
Co-leader Tariana Turia says there are also still issues to discuss with National, and take back to supporters to discuss.
"It'll probably be Monday or Tuesday of next week before we'd have any very clear decision about what role, if any, that we might take."
Before the meeting Mr Key said he would be able to work with the MPs even if no arrangement is made with them.
Mr Key told Morning Report he started the process of forming a relationship with the Maori Party two years ago, when he became leader.
"Bill English and I have been meeting Tariana Turia and Pita Sharples on a reasonably regular basis - I think that's been progressing quite well.
"I was always confident if the Maori Party held the balance of power there would be at least a reasonable chance that we would have a shot at putting together a Government with them in some form."
National has enough seats to govern with the support of ACT and United Future, after its sweeping victory in Saturday's election.