Members of the council said he received the most support for the job in the second secret-ballot, a previous poll having been held in July.
Mr Ban finished ahead of UN Under Secretary General for Public Affairs Shashi Tharoor of India and Thai Deputy Prime Minister Surakiart Sathirathai.
But the race remains wide open with more candidates expected to enter the fray.
In Thursday’s “straw poll” Jordan's UN Ambassador Prince Zeid al-Hussein came in fourth, having only entered the race on September 5.
"It was the same order (for the top three) as in July," Argentina's UN Ambassador Cesar Mayoral told reporters.
His Chinese colleague Wang Guangya later confirmed Ban's victory, saying he was now clearly the front-runner.
"Things can always change, but now he is leading," Mr Wang said.
The contenders
A career diplomat, Mr Ban served as Seoul's chief envoy to the world body from 2001 to 2003 and also acted as the chief secretary to former UN General Assembly president Han Seung-soo.
The 62-year-old foreign minister also previously served at South Korea's embassy in Washington.
Prince Zeid's fourth place came as a surprise and a disappointment to many diplomats due to his late entry.
Previously the leadership race was widely viewed as a lackluster field and the Prince Zeid's entry fueled expectations that he could emerge as a viable compromise candidate.
The 15 members of the council had three options to signal their opinions of the five contenders: "encourage", "discourage" or "no opinion."
Sources said Mr Ban received 14 encouragements and one discouragement while Mr Tharoor got 10 encouragements, three discouragements and two abstentions.
All five declared candidates hail from what the United Nations regards as the Asian region amid a consensus here that it is now Asia's turn to assume the world body's top job in line with an unwritten rule of regional rotation.
Asia has not had a UN chief since Myanmar's U Thant finished his second term in 1971.
Third ballot planned
Despite Mr Ban's current front-runner status, some diplomats said the council hoped to see some of the declared candidates drop out and stronger candidates throw their hats into the ring.
"Anyone can join the race as long he is recommended by his government," Mr Wang said.
Greece's UN Ambassador Adamantios Vassilakis, the current president of the council, told reporters that he planned to convene another informal meeting on Mr Annan's succession late this month.
He said he would present his council colleagues with several proposals, including having another straw poll or a formal vote.
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.
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 favorite.
The United States and some other Western powers have meanwhile made it clear that they want the best qualified person for the job irrespective of national origin.