And Act MP David Seymour believes the party could have a deal signed very quickly.
Leadership teams from both parties held their first meeting with re-elected Prime Minister John Key and his leadership team on the ninth floor of the Beehive amid other momentous events around the complex following Saturday's election.
United Future leader Peter Dunne had his first meeting with Mr Key on Monday.
Mr Key gave the strongest hint yet that Mr Seymour would get a ministerial portfolio despite being a new MP, because it would give the party greater resources -- "otherwise we'd have an MP pretty much on his own with an [executive assistant] and it is very difficult to manage that party-to-party relationship".
Mr Seymour is expected to get Associate Education Minister, responsible for partnership schools, the official name for charter schools negotiated by Act in the last Government agreement.
Mr Flavell is expected to be offered the role of Minister of Maori Affairs and the party will almost certainly seek an expansion of the Whanau Ora approach to social service delivery.
He thought an agreement could be concluded by the end of the week.
With 61 MPs, National has the numbers to govern alone but has invited its previous support parties, Act, United Future and the Maori Party, to enter confidence and supply agreements.
Upstairs in the Labour caucus room, leader David Cunliffe and his depleted team began their post-mortem of the worst election result for Labour in 92 years.
Mr Key told reporters he did not believe Mr Peters would want him to formally offer him anything, given that he had asserted his new role to be the leader of the Opposition. There was no "bad blood" there.
"But over time I do want to try and build a stronger relationship with New Zealand First and that is more likely to happen now on a case-by-case individual basis but I think there are areas [where] we can potentially work together but it will be a three-year process I think."
- By Audrey Young of the New Zealand Herald
