National deputy Nicola Willis has told RNZ she is not in the running for the deputy prime ministership.
"It's for the prime minister to decide and I've made it clear to him I don't have any expectation whatsoever of getting it."
Willis said she was happy to just "get on", form a government, and do her job as finance minister.
She earlier told reporters at Wellington Airport that she was comfortable with either David Seymour or Winston Peters getting the role.
Some of National's top-ranked MPs, including Willis and Chris Bishop, have flown to Wellington this morning, in further signs a deal for a new government is near.
With the parties yet to confirm final signoff, agreements could be signed as early as Thursday. Leader Christopher Luxon on Monday claimed the policy details of the deals with both ACT and NZ First were only waiting to be corroborated by one another, with ministerial and Cabinet positions remaining to be negotiated.
'My work here is done'
Willis, the deputy leader - who Luxon has promised the Finance Minister role - told RNZ at Auckland Airport on Wednesday morning those discussions were ongoing - but, asked what her departure meant, said: "it means that my work here is done".
"I just want the same thing that everyone in New Zealand wants, which is for us to get on, have some agreements signed, and form a government."
On landing in the capital, Willis said she hoped a deal was almost there but had no specific updates. There were no plans at this point for the caucus to meet on Wednesday, she said.
"This is where my family live. I have four children: 13, 12, 10 and eight and they're pretty keen to see their mum."
She said she did not know if a deputy prime minister had been agreed on, when reporters asked if she would be comfortable with either ACT leader David Seymour or NZ First leader Winston Peters in the role.
Bishop, a senior MP and member of National's negotiating team, said his departure was not a sign a deal had been done - more a matter of laundry.
"I've run out of clothes, I'm currently wearing Christopher Luxon's shirt," he told a surprised RNZ reporter at Auckland airport.
"He lent me a blue shirt," explained Bishop.
It did not mean a deal had been signed, he insisted, "it just means I've got to go home, I've been away for three and half nights and I was up here for one".
Landing in Wellington, he told reporters the talks were progressing well, but said Parliament would be unable to sit next week.
The first sitting days would "depend on the quickness of the governing arrangements being reached, so it's all a bit in flux but it won't be for some days".
"It's not going to be next week because we're, what are we now, Wednesday morning, yeah it's not going to be next week. There's a variety of things that have to happen for the House to sit so it's not going to be next week."
Party president Sylvia Wood was also seen at Auckland Airport this morning.
National's education spokesperson Erica Stanford, asked why she was arriving in Wellington on Wednesday afternoon, said she had private meetings to attend that were nothing to do with the negotiations.
"I haven't heard anything, I'm not in the inner circle, I've got nothing to tell anyone, sorry."
She said she had heard nothing so far about whether she would have the Education portfolio in Cabinet.