National's Jonathan Coleman has ruled himself out of the contest to replace Bill English.

The former health minister was considered a possible runner in the party's leadership race, but on Thursday confirmed he would not be standing.

"I think we've got three great candidates and I've made my decision on the basis of who is going to be best to beat Labour in 2020. I think that person is among those three," he told reporters.

He declined to say who he would be backing.

That leaves relative dark-horse Mark Mitchell and National Party veteran Steven Joyce as the remaining two members who may join confirmed candidates Amy Adams, Simon Bridges and Judith Collins in the race.

The trio announced their bids on Wednesday.

But while Selwyn MP Ms Adams made her announcement flanked by four supporting MPs, plenty were staying tight-lipped on who they would back.

"I'm taking my time," Todd McClay told media.

"I'm going to take some soundings but I'm not going to do that through the media."

Brett Hudson had a similar attitude.

"There's some way to go before we make a final decision," he said.

Mr English's resignation takes effect on February 27 and the 56-member caucus has to elect a new leader before then.

There will be a secret ballot, with low-polling contenders dropping out until one has a clear majority.