South Korea's candidate is apparently the frontrunner, although major powers are yet to reveal their hands.
As Mr Annan prepares to host his final United Nations General Assembly next week before retiring at the end of the year, South Korean Foreign Minister Ban Ki-Moon is basking in his second "straw poll" victory in the race.
But, diplomats say, the intrigue is far from over, with more candidates expected to emerge, and plenty of international diplomatic horse-trading to come.
Mr Ban finished ahead of UN Under Secretary-General for Public Affairs Shashi Tharoor of India and Thai Deputy Prime Minister Surakiart Sathirathai, in his second straw poll win since July.
Jordan's UN Ambassador Prince Zeid al-Hussein, who entered the race to succeed Annan last week, came in fourth ahead of former UN disarmament chief Jayantha Dhanapala.
All five declared candidates hail from what the United Nations regards as the Asian region amid a UN consensus that it is now Asia's turn to assume the world body's top job in line with an unwritten rule of regional rotation.
The United States and certain other Western nations have said they would like to find the best qualified person for the job, regardless of where he or she comes from.
Asia has not had a UN chief since Myanmar's U Thant finished his second term in 1971.
Despite Ban's current front-runner status, some diplomats said the council was hoping to see some of the declared candidates drop out and stronger candidates throw their hats into the ring.
Under UN Charter rules, the secretary general is elected by the 192-member General Assembly under recommendation from the Security Council, whose five permanent members - the United States, China, France, Britain and Russia - have veto power.
On Friday, Estonia, Latvia and Lithuania officially put forward Latvian President Vaira Vike-Freiberga as a candidate to succeed Annan.
The 68-year-old would become the first woman secretary general in the world body's 61-year history, but her chances of winning appeared slim.
In practice, the five permanent members have dominated the secretary general succession process.
And several diplomats said the winner will have to be acceptable to both the United States and China.
The buzz on the diplomatic circuit is that Goh Chok Tong, former prime minister of Singapore, has the required stature to win if he chooses to run.
Singapore's ambassador to the United States Chan Heng Chee was also viewed as another attractive candidate and according to Time magazine as a US favourite.
Greece's UN Ambassador Adamantios Vassilakis, the current president of the council, told reporters that he planned to convene another informal meeting on Annan's succession late this month.