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.