Social Housing Minister Paula Bennett is "quietly confident" she has enough support to become the National Party's deputy leader, she says.
So far, 23 National MPs have declared they will support Mrs Bennett, with 10 backing Transport Minister Simon Bridges.
Mr Bridges told Checkpoint with John Campbell he believed there was a "rump" within the caucus who were undecided.
"I think it's close," he said.
"There are still clearly people who will want to assess what the arguments are."
Mrs Bennett and Mr Bridges will go head-to-head in a caucus vote on Monday - they need 30 of 59 votes to get the job.
Bennett quietly confident
Mrs Bennett was in west Auckland this morning opening a new social housing development. She said while she was not crunching the numbers, she was quietly confident she would have the backing of enough of her caucus colleagues to win Monday's vote.
Among those who back Mrs Bennett are Justice Minister Amy Adams, Education Minister Hekia Parata and Auckland Central MP Nikki Kaye.
"I've certainly seen people coming out in the last few hours, yesterday afternoon, and this morning in support of me, but I just want to keep talking to them and putting myself forward," she said.
If she gets the job, Mrs Bennett will be the first Māori woman to hold the second most powerful position in government.
As well as holding the social housing portfolio, Mrs Bennett is the State Services Minister, the Minister for Climate Change Issues and Associate Finance Minister.
She said she had what it took to be Mr English's number two.
"I think I've proven myself to be a hard worker and someone that's really competent at what I do; given an opportunity I step up into it."
Bridges feels he has support
Mr Bridges was on the other side of town in Glen Innes, opening the first section of what would be Auckland's longest cycleway.
He said it would be a close contest that would go down to the wire.
"It's close. I mean, I'm not going to give you numbers because I think that's something that moves and changes literally day by day.
"But I do feel good about it and I do feel like I've got a sense of support and momentum in my campaign."
Several backbench MPs took to social media this morning to declare who they supported, but most cabinet ministers are keeping their votes close to their chest.
Mr Bridges said he had a good working relationship with Mr English.
"On these Auckland transport issues... these are thing that Bill and I have done a lot together on and I'm confident that we could work well together."
Mr English has not endorsed either Mrs Bennett or Mr Bridges, but described them both as excellent candidates.
Key wraps up last PM engagements
Meanwhile, John Key has opened a new i-Site visitor centre in Christchurch's newly refurbished Arts Centre, in one of his last engagements before finishing as Prime Minister.
Mr Key, the Tourism Minister, noted the tragedies and sacrifices the people of Canterbury endured for the past six years.
He paid tribute to Christchurch Mayor Lianne Dalziel and rebuild minister Gerry Brownlee for their work and leadership post-earthquake.
Christchurch is Mr Key's hometown.
His engagements tomorrow include a special needs Christmas party and the Auckland wedding of National MP Simon O'Connor.
On Sunday he plans to clear out his office in the Beehive, to make way for the incoming Prime Minister, Bill English.