Mr Peters was "the perfect politician", Ms May said. "He's so well known, he's so well liked. He doesn't actually do anything."
Five people are understood to be interested, including Mark Osborne, who was soundly defeated by Mr Peters last year.
Mr Osborne confirmed he was considering a second tilt, but had not made a final decision. He was "not at all" put off by his bruising first encounter with Mr Peters: "It's not going to be an easy challenge by any stretch of the imagination."
Others understood to be keen include Kerikeri doctor Chris Reid, former police officers Matt King and Darren Edwards, who now works for the Far North District Council, and businessman Ken Rintoul.
Dr Reid moved to Northland from Britain about 10 years ago after serving as a GP and a decade in the Royal Marines, including time with the Royal Navy's special forces. A keen photographer, he published a book last year of photos of his patients.
Meanwhile, National's byelection promise to upgrade 10 one-way bridges in Northland - a pledge widely mocked as pork-barrel politics - is still a point of contention.
Yesterday, NZ First transport spokesman Denis O'Rourke said only three were included in the next transport plan for Northland. Transport Minister Simon Bridges was adamant the bridges would be delivered within a six-year timeframe, even if the Government had to dip into funding other than the Land Transport Fund.
However, he did have one backtrack to make, finally admitting that putting two lanes on the Darby and Joan Bridge between two kauri trees in Waipoua Forest was "marginal". Claire Trevett