Prime Minister Helen Clark says it is unlikely she will be approached to become Secretary-General of the United Nations because she is the leader of a small country.
But it is clear that she would accept if asked.
She was named by Time this week as a possible contender, and while appearing to dismiss the reports, has never ruled them out.
However she has ruled out making any declaration of candidacy.
"I'm ruling out Helen Clark standing out there and saying, 'I think I'll offer myself'," she said on Sky TV's Williams Upfront on Thursday.
Asked if she would put her name forward, she said: "It's very unlikely that one would be approached. I am the Prime Minister of a little country of four million people. To the best of my knowledge, I am not in."
Kofi Annan's second term ends at the end of the year and the General Assembly has to agree on a Security Council recommendation by then.
In the informal rotation system that operates, it is Asia's turn to hold the position. But there is no clear winner among those who have declared an interest.
New Zealand's former ambassador to the United Nations, Terence O'Brien, said the formal campaigning several countries were engaging in was not normal. "Normally names are mentioned and discreet soundings are taken and, with some massaging behind the scenes with influential people and influential countries, names float to the top."
But when no clear candidate emerged, compromise ones were found as with Mr Annan's predecessor Boutros Boutros-Ghali 10 years ago.
Mr O'Brien believed Helen Clark had the ability and credentials, even though the post had never gone to a former Prime Minister.
"On the other hand, the system is so desperately in need of a shake-up that everybody could rally behind a political figure, and New Zealand and Clark on those grounds would be quite a sound choice."
Any candidate needs the support of the 15-member Security Council and its five permanent members - the United States, China, France, Britain and Russia - which have a veto.
Helen Clark rejected a suggestion that her "anti-American stance" would hurt her.
"I don't have an anti-American stance; I have a pro-New Zealand stance. I recognise the US as a very, very, very close friend of New Zealand but I am my own person and New Zealand is its own country."
Opposition leader Don Brash has said he would support any bid by Helen Clark for the job.
Clark 'unlikely to be approached' for UN position
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