First-term MP Chris Luxon has put his hat in the ring for the National Party leadership and is believed to have the edge when it comes to numbers, but talks with some MPs are ongoing.
Only former leader Simon Bridges has openly declared his candidacy.
Luxon had not confirmed whether he would enter the race, which opened up last Thursday when then-leader Judith Collins was ousted following a no-confidence vote.
Pro-Luxon MPs had been trying to talk him into running, and former leader John Key was also making the case over the weekend in conversations with MPs.
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Now, it appears Luxon has made up his mind, and has the edge on numbers.
Luxon has said he will not comment on the leadership race until after caucus meets to elect the leader on Tuesday afternoon.
Caucus has expressed a preference that the contest not go down to an election on Tuesday, and that the candidates winnow themselves down to one who will effectively be anointed at that meeting.
But this would require a deal to be done between the two frontrunners behind the scenes, possibly involving Bridges being given the finance portfolio.
But as of Sunday evening, no such deal had been done.