The Takfiri group in a statement said that with the death of al-Baghdadi, whose real name was Ibrahim al-Samarrai, it would soon announce its new "caliph”, according to al-Sumaria news website.
Daesh in the statement also called on its members to stay in their bases and "continue resistance”.
The announcement came one day after Iraqi Prime Minister Haidar al-Abadi declared total victory over Daesh in the northern Iraqi city of Mosul.
The so-called Syrian Observatory for Human Rights, a monitoring group affiliated to Syria’s foreign-backed opposition groups, has also said that it has "confirmed information” that Baghdadi has been killed.
Following the announcement by Daesh, another local source revealed that an internal revolt and infighting had broken out within Daesh ranks in Tal Afar.
The source added that a wide-scale arrest campaign was launched against supporters of Baghdadi.
According to the report, a curfew was also declared in most of the city.
No Iraqi official has confirmed the report yet.
The report comes weeks after Russia said it was "highly likely” that the Daesh leader had been killed in an airstrike carried out by the Russian Air Force in Syria’s Raqqah city in May.