Both Labour and National are holding their first caucus meetings at Parliament today as they get ready to start negotiating with New Zealand First to try to form a government.
New Zealand First leader Winston Peters is in Auckland and was due to arrive in Wellington tomorrow to meet with his new caucus.
National Party leader Bill English said he would name his negotiating team after consulting with Mr Peters later this week.
"There's ongoing discussions just about the practicalities of organising a meeting in the next couple of days.
"Mr Peters has been up north and he's travelling, I don't think we would get too concerned about the way things are moving."
National's deputy leader, Paula Bennett, appeared relaxed about giving up the role of deputy prime minister should National and New Zealand First form a government.
"Oh I'm not too bothered to be honest, I love what I do, I'd still be deputy leader of the party and that's the main thing really, so we'll just work our way through it."
She said she did not expect to be part of the negotiating team as she had not spent much time with Mr Peters.
"I kind of don't have a relationship [with him], there's nothing wrong, there's just no relationship there."
National's negotiating team would be likely to include senior MPs Gerry Brownlee and Todd McClay.
No decisions yet on negotiating team - Labour
Labour today welcomed 17 new MPs, having won 13 extra seats at the weekend's general election.
On his way into caucus this morning, the party's former leader, Andrew Little, said he did not expect to be on Labour's negotiating team, saying it was not a decision for him to make.
His colleague David Parker said no decisions had been made about the negotiating team but did say he had a good relationship with Mr Peters.
"I've got respect for Winston Peters, he's our longest serving MP and I find him trust-worthy."
Questions re-emerge over Peters' superannuation leak
The discussions around who would or would not be on the National Party negotiating team has led to questions resurfacing about who leaked details of Mr Peters' superannuation overpayment.
The Inland Revenue Department, Department of Internal Affairs and the Ministry of Social Development have all ruled out the leak coming from them.
National Party chief of staff Wayne Eagleson who was among those in government who were told officially about the overpayment, said it did not come from him or the National Party.
Mr Eagleson confirmed yesterday he had resigned from the role, and would leave once negotiations to form a government were complete.
He remained adamant the party did not leak information about Mr Peters' superannuation overpayments.