THE United Nations Security Council has quietly begun the formal process of selecting the world organization's next secretary-general.Voting could begin next week. UN diplomats do not expect a clear winner in the first round. They predict a series of secret ballots that will select a list of finalists. The first problem, diplomats say, will be to decide whether to give priority to a list of nominees submitted by the Organization of African Unity. While there is no rule about geographic rotation for the post, Africa has never been represented, and many believe it is Africa's turn. A ranking American diplomat says the United States hopes the Council will agree on a short list of three or four candidates, to "avoid acrimony." But the search must be for the "best qualified" candidate, he says, adding that the US has "no institutional memory" of promising in 1980 to support an African in the next elections. Until now, the Council's five permanent members - the US, Soviet Union, Britain, France, and China - have controlled the selection process. This time, however, nonaligned members of the Council could vote as a bloc to influence the final vote. The foreign ministers of the five big powers met in New York last week. Diplomats say the five were most interested in: * Prince Sadruddin Aga Khan, a citizen of Iran, France, Pakistan, and Kenya. * Boutros Boutros Ghali, Egypt's deputy prime minister. (See story below.) * Bernard Chidzero, former finance minister of Zimbabwe. * Gro Harlem Bruntland, prime minister of Norway. * Gen. Ali Alatas of Indonesia. "There is [now] no outstanding candidate round whom everybody is rallying," British Foreign Secretary Douglas Hurd told reporters at the UN earlier last week. Javier Perez de Cuellar, the current secretary-general, finishes his second five-year term Dec. 31. The US has been noncommittal about its preferences thus far. Various reform proposals calling for a more streamlined UN system have been discussed informally at the UN in recent months. Members have discussed drastically reducing the number of high-ranking officials who report directly to the secretary-general. The first woman candidate for the post, Norway's Prime Minister Gro Harlem Bruntland, urged continued UN reform in a General Assembly address last week, including strengthening the UN chief's role in preventive diplomacy. But the idea of imposing reform before a new secretary-general takes office is meeting resistance. Nigeria's ambassador, Ibrahim Gambari, speaking for the UN's African group, said the new UN chief's hands should not be tied in advance. Mr. Perez de Cuellar himself spoke out against imposed changes: "Member countries, before trying to improve the Secretariat, should read the Charter of the UN. In the Charter, it says very clearly that the secretary-general is the chief administrative officer. It is not for the General Assembly to violate the Charter by trying to impose on the secretary-general the way in which he has to administer the House." IF the member states really want to help, Perez de Cuellar added, they should coordinate their efforts better and pay their dues, a legal obligation. The US is the UN's largest delinquent, owing nearly $500 million for the regular budget and peacekeeping operations. From all indications, the French are prepared to veto any candidate who does not speak French. This follows, France argues, from the UN Charter, which gives French and English equal weight as official UN languages. Egypt's Boutros Boutros Ghali is the African candidate thought to have the broadest support; he also speaks French. Uganda's former ambassador, Olara Otunnu, who engineered the 1980 compromise by which Perez de Cuellar was elected after a series of deadlocked ballots, is frequently mentioned as an unofficial candidate. Mr. Otunnu now heads the International Peace Academy in New York. Both France and the US are thought to have Prince Sadruddin Aga Khan high on their lists. He is considered to have style and energy, as well as experience in the UN system, although some have criticized his performance in previous duties. In any case, Nigeria's Ambassador Gambari pointed out at a recent news conference that while the Secretary-General is nominated by the Council, the final vote is cast by the General Assembly. "It need not be a rubber stamp," he said, noting that 51 out of 166 the Assembly's member states are African.