Azevedo has served as the WTO chief since September 2013, and his second four-year term started in September 2017.
Bloomberg reported that one of Azevedo's four deputies — Yonov Frederick Agah of Nigeria, Karl Brauner of Germany, Alan Wolff of the United States and Yi Xiaozhun of China — might serve as an interim caretaker until the end of his term in 2021.
The report comes as the WTO is coming through a crisis in its system for resolving disputes between its members after Washington paralysed it by blocking new appointments to the seven-member Appellate Body last year.
US President Donald Trump said that the WTO needed a major reform and suggested that Washington might withdraw from the organisation.