Options range from a full coalition inside Cabinet, a support agreement offering confidence and supply in return for some ministerial posts outside Cabinet, to sitting on the cross benches offering support on a case-by-case basis in return for minimal policy gains.
National and Labour have worked through what policies and positions they could offer in return for NZ First support and today's initial talks are a chance to float some of those and hear what Peters wants.
Peters has stressed he wants to wait for the special votes to be announced this Saturday before finalising talks, but has committed to making a decision by next Thursday.
Yesterday Labour leader Jacinda Ardern said that timeframe was possible, but to meet it preliminary talks would need to be meaningful.
"I think it is absolutely possible to do it within that timeframe. But it does mean those preliminary discussions are very important.
"The special votes remain important. But having this preliminary discussion means we will be able to move quickly once those special votes come in."
Ardern will be joined by deputy leader Kelvin Davis and other senior MPs.
"I'll be making sure that I bring those who are able to make sure that we shape policy priorities together," Ardern said.
Lawyer Brian Henry has been named as a possible member of NZ First's negotiating team but he will not be leading the talks - it's understood Henry has a lengthy trial on in Auckland. The team could include MPs Clayton Mitchell and Fletcher Tabuteau.
In preliminary results National won 58 seats, Labour and the Greens won 52 combined, and NZ First won nine. In a 120-seat Parliament in which 61 is required for a majority, Labour and the Greens and NZ First have only 61.
The special votes - about 15 per cent of the total - usually favour the Greens and Labour. Ardern said she was hopeful the Labour-Greens bloc would pick up at least one extra seat.
"I think it is fair to assume that we will see a one-seat uplift. I believe the Greens are probably closer to bringing in one more.
"Having a bit of extra comfort would certainly be helpful. But we should also keep in mind the numbers that National have worked on in the last several terms of Government. At any given time they have required ... a supply and confidence agreement to get their legislation through. So a small buffer is not unusual in New Zealand."
English met with a member of the Green Party's post-election negotiating team yesterday - but the context was rugby and not the possibility of a so-called "teal deal".
Green Party campaign committee member Andrew Campbell was named in the party's negotiating team last week.
His day job is senior media relations adviser for New Zealand Rugby, and it was in that role that Campbell met English at Parliament, accompanying members of the World Cup-winning Black Ferns.
Greens leader James Shaw this week dismissed talk of a possible Green-National deal as "noise and no signal".
