The Syrian Observatory for Human Rights, a longtime monitor of the country's conflict, said it had information from top IS leaders confirming Baghdadi's death.
The report could not be independently verified and Baghdadi has been reported dead several times.
But if confirmed, his death would mark another devastating blow to the jihadist group after its loss of Mosul, which Iraqi Prime Minister Haider al-Abadi said Monday had been retaken from IS after a gruelling months-long campaign.
"We learned of it today but we do not know when he died or how."
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Deir Ezzor, in eastern Syria, remains largely under IS control even as the group is losing territory elsewhere in the country and in neighbouring Iraq.
Abdel Rahman said Baghdadi "was present in eastern parts of Deir Ezzor province" in recent months, but it was unclear if he died in the area or elsewhere.
The US-led coalition said it could not verify the Observatory's information.
"We cannot confirm this report, but hope it is true," said coalition spokesman Colonel Ryan Dillon.
"We strongly advise ISIS to implement a strong line of succession, it will be needed," he added, using a different acronym for IS.
There have been persistent rumours of Baghdadi's death in recent months, and Russia's army said in mid-June that it was seeking to verify whether it had killed the IS chief in a May air strike in Syria.
With a USD 25 million US bounty on his head, Baghdadi has kept a low profile and was rumoured to move regularly throughout IS-held territory in the area straddling Iraq and Syria.
The 46-year-old Iraqi-born leader of IS has not been seen in public since making his only known public appearance as "caliph" in 2014 at the Grand Mosque of Al-Nuri in Mosul.
IS destroyed the highly symbolic site before Iraqi forces could reach it as they pushed the jihadist group from Mosul.
Abadi announced in Mosul yesterday that the campaign had ended with the defeat of IS in the city, hailing "a victory over darkness, a victory over brutality and terrorism".
The cost of victory has been enormous: much of Mosul in ruins, thousands dead and wounded and nearly half the city's population forced from their homes.
In Mosul's Old City, where buildings lie in ruins and burned-out cars and other debris choke the streets, security forces were still searching for remaining IS fighters.
"There are groups that are hiding in shelters," but they surrender or are killed, Aridhi said.
Since the Mosul operation began in October, 920,000 people have fled their homes, only a fraction of whom have returned, according to the United Nations.
Rights group Amnesty International on Tuesday accused Iraqi forces and the US-led coalition of exposing civilians to "relentless and unlawful attacks" in west Mosul.
"Pro-government forces launched barrages of indiscriminate or disproportionate attacks using explosive weapons unsuitable for such a densely populated urban area," Amnesty said.