"If there's enough support for the style of leadership that I have, it will be interesting," Miss Clark said.
No woman has ever headed the UN. Current secretary-general Ban Ki-moon was re-elected in June 2011. His second term is due to finish in two years.
Miss Clark told the Guardian she chose to ignore scrutiny around her looks relatively early on in her career.
"There was a lot of very gender-based criticism. You know 'Your voice is too low, your teeth are crooked'. They don't like your hairstyle, they don't like your clothes.
"In fact, they don't really like anything about you, and maybe this all adds up to [the notion] that they don't really like a woman doing what you're doing.
"But, you know, if you found all that hurtful then you're probably not going to be able to survive these jobs. You have to be able to dismiss it, and I seem to have developed a style, where [journalists] always knew that I'd get to a point and say 'move on', you know, 'get over it'," she said.
Miss Clark also gave her take on the political landscape in New Zealand, commenting on the fact there were fewer women in Government than when she was in charge, as well as the lack of women at the recent World Economic Forum in Davos, which she attended.
Finance minister Bill English represented New Zealand at the meeting, of which only 15 per cent of attendees were women, the Guardian reported.
"These battles never go away," Miss Clark said.
"It shouldn't just depend on a group of exceptionally ambitious women. We need it to be in the culture of our societies, institutionalising it in the normal scheme of things. [Then] there will be a lot of women at the top."
