Helen Clark British bookie's favourite to win Secretary-General X Factor

Helen Clark has been made the favourite for the United Nations' top job by a British bookmaker - as one of her main rivals impresses with her pitch for the Secretary-General position at UN headquarters in New York.

After formally announcing her bid for the Secretary-General position last week, Clark was given odds of 7/2 by betting company William Hill, making her joint favourite with Bulgarian politician and Unesco Director-General Irina Bokova.

The betting company has now updated its odds to make Clark the favourite at 5/2 (a 29 per cent chance of winning), ahead of Vuk Jeremic, former President of the UN General Assembly, at 4/1 (20 per cent), and Bokova at 9/2 (18 per cent).

The race for the job intensifies this week, with each of the candidates getting an individual two-hour session at the United Nations General Assembly in New York. Each is also asked to submit a written statement of up to 2000 words.

The sessions - dubbed "Secretary-General X Factor" - will be a crucial test in their bids to show their talents and win favour for their candidacies.

Former Prime Minister Clark will have her turn on Friday at 3am New Zealand time. She is now one of eight candidates who have been nominated by their countries to replace Secretary-General Ban Ki-moon when his term expires on December 31.

It is not expected that the sessions this week will result in any formal resolution of a favourite but the forum is designed to inform the selection process.

Bokova presented to the UN overnight New Zealand time, and according to the AAP she was "impressive", and gave answers in English, French or Spanish, depending on the source of the query.

A key selling point was her record in raising the number of women in senior level positions at Unesco, from 24 per cent to almost 44 per cent.

The appointment will be made by the General Assembly later in the year, on no fixed date, on the recommendation of the Security Council.

The selection process will shift to the Security Council in July when the first straw vote -- by secret ballot -- will be held among the 15 council members.

There are no hard and fast rules but if voting is similar to previous selections, each of the 15 countries will be asked to give one of three verdicts on each of the candidates: encourage, discourage or no opinion.

The five permanent members, United States, China, Russia, Britain and France, have the power to veto any candidate.