National and ACT are "far through" an agreement on the terms of its coalition deal, 1News understands.
It follows the announcement of the official results of October's general election, which saw National lose two seats after special votes were counted.
It means New Zealand First's eight seats are required for National and ACT to form a government.
Last week, National leader Christopher Luxon said discussions with both ACT and NZ First would progress with "pace" now the official result was clear.
Peters also told 1News last week discussions with National were "going well".
Peters and ACT leader David Seymour have a well-documented dislike for one another's politics, something Labour and the Greens have pointed to as a possible thorn in the side of the three-party partnership.
Peters confirmed on Sunday he had ignored a text message from ACT leader David Seymour, saying he thought it was a "fake".
1News understands NZ First still had not returned Seymour's calls as of Monday afternoon.
Sources close to negotiations say its unlikely a coalition announcement will emerge in the next couple of days, and insiders were only hopeful it an agreement would be reached this week.
The NZ First caucus met in Wellington today, after Peters was greeted at Wellington Airport by a throng of reporters, whose questions he ignored.
Meanwhile, in Camp Labour, 1News understand a leadership vote is due to take place at a caucus meeting tomorrow morning.
Chris Hipkins could be elected unopposed. There will only be a contest if there’s a challenge to the leadership.
For that to happen, 60% of the Labour caucus would need to oppose Chris Hipkins' leadership.
As part of the party's constitution, Labour needs to have a leadership vote within three months of an election defeat.
On TVNZ's Breakfast this morning, senior Labour MP Ginny Andersen said she "100%" backs Hipkins to remain as leader following Labour's crushing defeat at the election.
Additional reporting by Felix Desmarais.
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