French Ambassador Francois Delattre, who holds the council presidency, said that he had set the date in a letter to the president of the General Assembly.
The 15-member council is expected to decide by October on a single nominee who will be presented to the General Assembly for endorsement before he or she succeeds Ban Ki-moon on January 1.
The decision however will ultimately come down to the permanent members — Britain, France, China, Russia and the United States — who have veto power in the council.
Delattre said that the council is “playing its full role in this crucial decision for the future of the United Nations.”
Eleven candidates, five of whom are women, are running for the top post, but diplomats expect more contenders to join the field.
Among the strong candidates are Argentine Foreign Minister Susana Malcorra, New Zealand’s former prime minister and head of the UN Development Program Helen Clark and Antonio Guterres, a former prime minister of Portugal who led the UN refugee agency UNHCR.
There have been calls for a woman to head the United Nations for the first time and Eastern European countries are pushing for a candidate from their region.
The head of UNESCO, Irina Bokova of Bulgaria, former Slovenian president Danilo Turk and Slovak Foreign Minister Miroslav Lajcak are among the eight candidates running from Eastern Europe.
During the vote, the 15 members of the council will be asked to indicate by ballot whether they “encourage”, “discourage” or have “no opinion” of a candidate.
The result of the vote will be communicated to the candidates, giving them an indication of the level of support they have in the council and whether they should withdraw from the race.
The search for a successor to Ban comes at a time of high anxiety in global affairs as the United Nations grapples with the biggest refugee crisis since World War II and raging conflicts in the Middle East and Africa.
In a shift from previous elections, the candidates this time around attended formal hearings at the General Assembly to lay out their vision for the job.
The hearings are part of an effort to inject some transparency to the selection of the UN chief, although in the end, the big powers will carry weight in the choice.