He would not say which of the three he would be supporting.
Meanwhile Collins told media today she would respect the wishes of the caucus by not having a public display of support from other National MPs.
Yesterday, Adams announced her candidacy with National MPs Nikki Kaye, Tim Macindoe, Maggie Barry and Chris Bishop by her side.
Asked why she wouldn't do something similar, Collins said: "I deeply respect the caucus decision on how to play this.
"The fact is that the caucus agreed that we would not come out and be counted in those sorts of things until after the vote. That was the advice of Bill English, and I'm sticking by it."
Bishop, however, said there was nothing to stop MPs endorsing candidates.
"It's obviously happened in relation to Amy. There may be others who come out over the next few days or the next week to endorse candidates.
"Just for me, I've made up my mind. I think Amy will make a great leader of the National Party and an outstanding Prime Minister."
Collins called on party members to let their MPs know their thoughts on the leadership.
Some of the backbench MPs should also have already been promoted, she said.
"We have, in our new intake and in 2014 and also 2011, some really good people who feel, quite rightly, they haven't been given a chance, and I think that in Opposition, that's the time to do it.
"But it should always be about merit ... It's about who can do the job. That's my bottom line for anything."
Collins said her best attributes were that she says what she thinks, she knows how to be effective in Opposition, and that she can beat Jacinda Ardern.
"I know what happens with Opposition, even the largest Opposition in history. Once you get through the winter and you start getting the Budget coming out, and a Government fulfilling some of its promises, it is tough. And you need to be significantly tougher than in Government."
Asked whether she could have Bridges or Adams as her deputy, she said it was a matter for the caucus.
Paula Bennett has said she wants to stay on as deputy leader.
Collins said the position was up to the caucus, adding "it's important we don't keep looking to the past, but we look to the future".
But she added that Bennett would not say she represented the past.
English announced his intention to retire from politics on Tuesday. A new leader is expected to be anointed on February 27.
The party's constitution simply calls for the caucus to choose a leader, and outlines no process that must be followed.
A possibility is that MPs will vote, and then the least-favoured candidate will drop out of the race after each voting round until one candidate has a majority.
MPs have said that it will be a secret ballot.