But the Prime Minister has said he has received no advice of her intentions, which suggests she has not quite made her decision.
If she goes ahead and takes the plunge her home Government will be among the first to know because she will need its active support.
John Key and his ministers and officials worked hard to help Helen Clark become the head of the UN Development Programme after her election defeat. They would have to lobby other Governments doubly hard for her to get the top job.
The effort could be more expensive than any campaign New Zealand Governments have previously financed for an international office.
But it would be worth it for New Zealand and, dare we say, for the UN too.
The organisation's image depends crucially on the Secretary-General. It has lost some lustre since Ban Ki-moon took over from Kofi Annan.
Conspicuous energy and statecraft, though, might not always be the qualities wanted by most UN members, or at least the most powerful UN members.
Helen Clark's reference to her "style of leadership" is recognition that this is not like previous elections she has faced. Competence, commitment and drive might not be enough; in fact, they could count against her if most countries want the UN to stay on the sidelines of conflict and genocide.
Her prospects might be enhanced by the fact President Barack Obama should be still in the White House in 2016 when the next Secretary-General is appointed. He might resist pressure from Israel, which would have resented the exposure of two spies' attempts to obtain New Zealand passports when Helen Clark was in power. Arab-Israeli issues are never off the UN's agenda.
If the UN wants a woman to be its next head, it can hardly ignore the woman heading its largest agency. It is hard from outside to judge the work she has done at the UNDP but knowing her, she will have the measure of its bureaucracy and politics.
She has the credentials for the big desk. She should run.