He added that New Zealand would provide the former Prime Minister with resources to conduct a campaign.
But there had to be a degree of realism, he said, because many in the UN still believed the selection was based on whose "turn" it is.
"There is no question she is an immensely credible candidate," he said. "It's about time in the 70-year history of the United Nations they had a woman in charge.
"She's amazingly capable."
She had had nine years running New Zealand and seven years running UNDP.
"The only point I'd make is that if she does put her name forward, there has to be a degree of realism because with all of these jobs, it can be very much who they think someone's turn is," Mr Key said this morning on TV3.
Helen Clark in New Zealand last week hinted an announcement was coming when she said "nothing to announce right now".
Speaking on Newstalk ZB, she said it should be about the best person for the job.
"It's all geopolitics in the end but let's hope the geopolitics is going to be informed by who is the best person for the job; what are the challenges now, what are the leadership and other skills required.
"I think that must be the central issue."
Ban Ki-Moon's term finishes in December and the appointment is made by the UN general assembly on the recommendation of the Security Council - on which five countries have a veto: US, China, Russia, Britain and France.
But the general assembly has demanded a more transparent process - it has sought nominations and will hold candidate forums in which candidates can be questioned by member states.
The first of those will be held in New York on April 13.
Seven nominations have been received so far.
Under the geographic rotation system, it would be Eastern Europe's turn but there is also a campaign to appoint a woman for the first time.
