The 15-nation council will hold a secret ballot on the four official candidates on Monday, unless the session is delayed by the conflict between Israel and Hizbollah, UN diplomats said.
"It's a beauty contest," said a British diplomat, describing the closed-door meeting which will sift the candidates in order of popularity. As the straw poll is anonymous, the support of the veto-holding powers will not be known at this stage.
"They won't be announcing 'and the winner is...'," the British diplomat said. Once the council's political support for one or two candidates becomes clear, the big powers will only hold a further straw poll, or call a vote, later in the year after consultations in capitals.
Mr Annan, a Ghanaian, will have completed two five-year terms as secretary general when he steps down at the end of this year. Asian countries have argued that it is "their turn", to claim the top UN job on the ground of geographical rotation. The US and Britain say the Security Council should pick the best man or woman for the job - and that means not necessarily from Asia. Two of the four contenders are current or former UN employees. Shashi Tharoor of India, the UN's undersecretary general for communications and public information, is a key adviser to Mr Annan, while Sri Lanka's Jayantha Dhanapala is also a friend of the secretary general and a former undersecretary general for disarmament.
The other two names in the hat are those of Thailand's Deputy Prime Minister, Surakiart Sathirathai, who was the first to declare and who has the formal backing of Association of South East Asian Nations, and the South Korean Foreign Minister, Ban Ki-Moon.
The candidates have been travelling the world, canvassing for support among the 15 Security Council members. But it is the five veto-holding powers - Britain, the US, France, Russia and China - which hold the crucial votes. Diplomats said that the big five have been playing their cards close to their chests. It could be that the name of the eventual successful candidate has not even been mentioned at this stage in the race. But names such as Tony Blair and Bill Clinton are not taken seriously because it is taken for granted that a UN secretary general will never hail from one of the Security Council's permanent members.
The UK is looking for a secretary general with enough clout to be able to pick up the phone to world leaders, as well as proven managerial skills, at a time when the UN's international standing is at a low ebb.
But the great unknown is the attitude of China, which has publicly declared that it wants the next secretary general to hail from Asia.
Each of the candidates in Monday's straw poll could be said to have at least one handicap. In the case of Mr Tharoor, it is his close association with the administration of Mr Annan as well as the fact that Pakistan can be expected to campaign against the candidacy of its rival India for the top post. It is not for nothing that the Security Council powers prefer small, trouble-free countries to provide their pool of candidates.
For Mr Dhanapala it is his age: he is 67, already two years older than the official UN retirement age.
Mr Ban Ki-Moon, who has assiduously courted Washington, has been criticised for his country's failure to call North Korea to account for its human rights abuses. He has also opposed a bid from Japan, a non-permanent member, in its campaign for a permanent Security Council seat.
Surakiart Sathirathai has not been a popular Foreign Minister at home, and is not noted as having staked out strong positions on human rights and democracy.
France has always insisted that the secretary general should speak fluent French, which could give the Thai and South Korean candidates a boost. But diplomats say that any successful candidate could go on a crash course.
Diplomats say the council hopes to have the appointment wrapped up by October. But at the UN, nothing ever goes to plan. After all, the US ambassador, John Bolton, said early in the year that he wanted a decision by June.
Veterans in the running
Jayantha Dhanapala
The Sri Lankan diplomat, 67, is a senior adviser to the President on the country's peace process. He is experienced in multilateral negotiations as the former UN disarmament chief. He also speaks Mandarin.
Shashi Tharoor
British-born Indian diplomat, 50, who is under-secretary-general for communications and public information at the UN. Ultimate UN insider with 28 years of UN experience on peacekeeping and humanitarian issues. A prolific writer.
Ban Ki-Moon
Veteran diplomat, 66, who has served as South Korea's Foreign Minister for the past two years and played a leading role in the six-party talks aimed at persuading North Korea to abandon its nuclear programme in return for incentives.
Surakiart Sathirathai
Thailand's Deputy Prime Minister and Foreign Minister is a diplomat and scholar, aged 48. Says he is ready to take difficult decisions on reform and believes in multilateralism. Both parents were educated in France.
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