The U.N. Security Council will use the last 10 days of July for its first informal straw poll on the likely successor, reports the Financial Times. Annan's term is over at the end of this year.
The council's 15 members will give their first impressions of the four Asians who have formally declared as candidates. They are India's Shashi Tharoor, Sri Lanka's Jayantha Dhanapala, Thailand's Surakiart Sathirathai and South Korea's Ban Ki-moon.
In the past, the job has been held largely by candidates from smaller countries.
The report said under an unwritten convention, citizens of the five permanent members of the Security Council cannot win the job.
Other likely candidates mentioned are Goh Chok Tong, Singapore's former prime minister, and Ashraf Ghani, Afghanistan's former Finance minister.