Abdul Hassib Seddiqi told the BBC's Afghan Service that Mullah Omar had died of health problems at a hospital in Pakistan.
Afghanistan's government says information on his death is "credible".
The latest reports of Mullah Omar's death are being taken more seriously than previous such reports. The Taliban is expected to issue a statement soon.
Sources at the Taliban's two main councils in Quetta and Peshawar in Pakistan told the BBC they were in intensive talks to agree on a replacement for Mullah Omar.
A statement from the office of Afghanistan's President Ashraf Ghani said that it believed, "based on credible information", that Mullah Omar died in April 2013 in Pakistan.(s:bbc)