Simon Bridges has not ruled out potentially putting his hand up for the Prime Minister's position.
The Transport Minister and Tauranga MP told NZME today: "I think I'm going to keep my powder dry and decide in there. I want a good discussion in the caucus room''.
''These issues are far too important to dealt with in the media."
MPs were in a high state of anticipation as they headed into Parliament this morning although the fevered lobbying has not yet begun.
Talking to reporters on the way into caucus, Key said he would leave the caucus meeting for the discussion on the leadership contest.
TVNZ political reporter Andrea Vance offered commentary from Wellington today, saying: ''Simon Bridges is the dark horse and he's clearly thinking about a run'' at the Prime Minister's position.
Meanwhile Bay of Plenty MP Todd Muller said he would welcome a contest.
He said it was too early to say if there was a mood for change "but I think there is probably an appetite for a contest so you can get a sense of where people intend to take the party over the next three years".
The comments come as competition appears to be growing for the National leadership after Prime Minister John Key announced his shock resignation yesterday.
Health Jonathan Coleman confirmed he was interested in putting his name forward and had been taking "soundings".
"Yes, I am interested but I've got nothing more to say at this stage. I would not put my hand out unless there was considerable appetite for a contest of ideas across the caucus.
"I've been taking some soundings - not doing numbers, but seeing what the appetite of caucus for a contest is."
Education Minister Hekia Parata said she would back English.
"I'm not precluding that there will be a contest, I'm just saying I think he is best for the role of that's what he decides to put his name forward for."
She said English offered predictability and certainty and was known for his sound management of the economy.
"I think he's got a great set of values."
She would not say if anybody else had rung her or who she would back for deputy.
Paula Bennett, who is Key's preference for deputy leader, said she would wait to talk to caucus before commenting.
She said she was "devastated" Key was leaving.
"He's the greatest leader I've ever known and ever seen and I'm just going to miss him. I'm going to miss him as a leader and miss him as a Prime Minister and miss him as a man."
National minister Judith Collins is still refusing to show her hand on the party's leadership as National MPs head into a caucus meeting for initial discussions on who will replace John Key.
Asked if she would put her name forward for a position, she said: "There's nothing to add at this stage."
She would not say if she had made any decisions yet. "We'll see."
Yesterday Key announced he was stepping down from Parliament and gave his backing to Bill English to replace him.
MPs are expected to hear an emotional explanation from Key about his decision at this morning's caucus meeting, which will set the rules about the contest to replace him.
English is expected to put his name forward and is the favourite given Key's endorsement.
English refused to speak to reporters before entering the caucus room.
Asked about a growing mood for change in the caucus, Key said "that's always a view that people will take but you could also say there's been one way of meaning things for the past 10 years, that's been me and Bill, and it's been a pretty successful 10 years."
Backbench MPs were reluctant to say whether they would back Bill English or whether there should be a contest.
Justice Minister Amy Adams refused to say if she would put her name forward. "It is something we will discuss in caucus and I'm not intending to play all that out in the media."
Senior cabinet minister Gerry Brownlee and the party whips will be taking charge of the election process, including setting a deadline for nominations.
English is expected to stand as leader although his dull long-winded performance at a press conference yesterday has worried some caucus members spoken to by the Herald.
Brownlee said National had "a very very calm" caucus at the moment and members were showing a high degree of maturity.
English is yet to confirm he will stand but those National MPs who were willing to state their views were backing English.
They included ministers Michael Woodhouse and Nathan Guy as well as backbencher Nuk Korako.
Guy said English would be a "fantastic" leader and Prime Minister but he would wait to see if English was willing to run.
"Bill English has steadied the economy through some very turbulent times, he's got the history of the party, he's worked incredibly well with John Key, he's got broad support across the business community and I think quite broad support across the New Zealand public."
He would not put his name up for the deputy position, but expected numerous people would want to contest it. "I'm not in a team."
He said it was too early to tell what caucus would do - many were still coming to terms with Key's decision and it was the first leadership change for many.
Backbench MP Alfred Ngaro said it was something many National MPs had not experienced before because Key had led the party for a decade.
"So for us it will be a good chance to hear what happens. We don't know who's going to put their names forward. We've never been in this situation before so we are going to allow the process to take place and see what happens."
He said there was "lots of talk going on".
"At the moment we want to acknowledge the Prime Minister for his leadership and we will do that this morning within the caucus. And then the debate begins."
David Bennett would not say who he was backing, but said Key's views would influence the caucus.
Parmjeet Parmar also declined to give a position but said English was "great". She said her preferred leader was "definitely John Key. But he's leaving."
MPs also said they had been shocked by Key's announcement. Parmar said she had not expected it. "It was really shocking."
A recent UMR poll asked which MP people favoured to take over from Key should he step down - a question various polls have asked over the years.
English received the highest support at 21 per cent; Steven Joyce 16 per cent; Paula Bennett 11 per cent and Collins 6 per cent.