Health Minister Jonathan Coleman, Finance Minister Bill English and Corrections and Police Minister Judith Collins have confirmed they will run as National Party leader to replace John Key.
Other contenders may yet still emerge before the party holds a caucus meeting on Monday to vote for a new leader.
Mr English, who has been endorsed by Mr Key, is seen as best-placed to win but some analysts felt Mr Coleman stood a chance.
"It's Bill English's to lose in the sense that there's such a strong endorsement and essentially direction from Key that it's very difficult for the caucus to outright repudiate the prime minister's preference," said Jon Johansson, a political scientist at Wellington's Victoria University.
Several Cabinet members, including Immigration Minister Michael Woodhouse and Primary Industry Minister Nathan Guy, have declared their support for Mr English.
Other potential candidates include senior Cabinet minister Steven Joyce, fellow Cabinet minister Paula Bennett and Energy Minister Simon Bridges.
A recent UMR survey of voters pegged English as favourite to replace Mr Key on 21%, followed by Mr Joyce on 16%, Ms Bennett on 11 percent and Ms Collins on 6%. Mr Coleman was not ranked in the survey, which was conducted in early October, but said he had youth and energy on his side.
Mr Johansson said some backbenchers felt senior party positions were all held by old hands and there was room for new blood.
"I think there could be a little bit more turbulence going on in that caucus than surface appearances," he said.
