"Then the formal process moves to July for the Security Council to start deliberating. When that will be finished, who knows."
The term of the incumbent, Ban Ki-Moon, expires at the end of this year.
Prime Minister John Key, who is from an opposing party and defeated her as Prime Minister, has said he would nominate her and campaign vigorously for her if she put up her hand.
It is an open secret that she would be a contender if she thought she had a chance but eyes are on the Eastern European group at present to see if they can settle on a consensus candidate.
Helen Clark is head of the United Nations Development Programme, No 3 in the UN hierarchy.
On a system of geographic rotations, it is considered Easter Europe's turn but there is also a strong push to appoint a woman to the position for the first time.
Eight candidates have been nominated so far.
According to UN rules, the position is decided by the General Assembly of member countries on the recommendation of the Security Council but the General Assembly has sought a more transparent selection process.
Helen Clark said the process "has months to run".
"You will see more people coming forward with their names. Yes there is a field now but I think the field will be larger."
New Zealand is part of the Western Europe and Other Groups.
She said she thought the contest was "wide open".
"The member states are very conscious that we live in extremely challenging times ... so I think that minds will be very much on 'what are the set of skills that the member states would like the new Secretary-General to have?'"
"There hasn't been a head of state, there hasn't been a head of Government, there have been a lot of foreign ministers - so there is really no rule around this. It is really what is deemed to be the consensus of member states at the time."
Asked if she was expecting former Australian Prime Minister Kevin Rudd to stand, she said, "I have no idea, no idea".
The Australian newspaper ran a piece at the weekend about Mr Rudd's prospects of getting the job.
It quoted former editor-in-chief Chris Mitchell talking about a visit he had had from Mr Rudd last November in which he had rated Helen Clark's chances highly.
"Rudd asked me if the newspaper would back him if he ran for the Secretary-General's job," Mitchell told journalist Pamela Williams.
"He said he thought the East European candidates would tend to cancel each other out or be vetoed by Russia, and Helen Clark would be the surviving candidate.
"He said his relationships with [current Prime Minister] Malcolm Turnbull and [Foreign Minister] Julie Bishop were strong and that if it came down to a run-off between himself and Clark, they would have to back a former Prime Minister."
Helen Clark was at Parliament in Wellington opening the Religious Diversity Centre, of which she has agreed to be patron.
But she won't be having talks with Mr Key, who is at present in Washington.
She returned to see her 94-year-old father, George, who had been unwell.
She would not answer questions again about the Trans-Pacific Partnership, which she supported when questioned in October last year.
Talking about the flag referendum, she said she voted but would not say which way.
