Clark's chances rest on whether Eastern Europe can come up with a consensus candidate, one acceptable to Europe, the US and Russia.
With the current crisis in relations over Ukraine, that is not a simple task.
If it can't find a consensus candidate, Clark will almost certainly seek the post and would be a front runner.
It would be pointless for her to publicly declare too early. To have done so this year could have interfered with New Zealand's campaign for a Security Council seat.
If there is a contest, candidates might still be reluctant to be first to declare because they are likely to attract comment and criticism.
Eastern Europe is being given time - and there is plenty of it, as the next term of the Secretary General begins in 2017.
In the meantime, Clark will continue what the Foreign Policy magazine termed a "stealth campaign".
None of the eight Secretary Generals has been a woman, and Clark has raised the issue in interviews.
The Western European and Others Group to which New Zealand belongs has supplied heads before, but not for 34 years, and all have been from the northern hemisphere.
Chile's President, Michelle Bachelet, is sometimes mentioned as a possibility, as is Brazil's President, Dilma Rousseff. But both were re-elected this year and would be sitting leaders.
The UN has never been headed by a former leader.
While Helen Clark is a former leader, her position as head of the United Nations Development Programme is establishing her administrative credentials.
The job also places her in a perfect position for her non-campaign; she is in constant contact with representatives and leaders whose support she would need but in a role that is not heavily politicised.
The Secretary General has been appointed in the past in a vote by the UN General Assembly on the recommendation of the Security Council - on which the five permanent members have a veto.
New Zealand will be on the council in 2016 when the decision is made, though it is hard to see that that would advantage or disadvantage any Clark candidacy.
But if Eastern Europe can find a consensus candidate, Helen Clark would have to accept that being at the right place at the right time in history isn't always enough.