Baghdadi's death, which has been frequently reported since he declared a caliphate from a mosque in the Iraqi city of Mosul in 2014, is one of the biggest blows yet to Daesh, which is trying to defend its shrinking territory in Syria and Iraq.
The Syrian Observatory for Human Rights (SOHR) said on Tuesday that it had "confirmed information" that Daesh leader Abu Bakr al Baghdadi has been killed.
"Top tier commanders from Daesh who are present in Deir Ezzor province have confirmed the death of Abu Bakr al Baghdadi, emir of the Daesh group, to the Observatory," SOHR director Rami Abdel Rahman said.
"We learned of it today but we do not know when he died or how."
Deir Ezzor, in eastern Syria, remains largely under Daesh 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 was killed in the area or elsewhere.
The US general who heads the coalition fighting Daesh said he had no information that would confirm or deny claims that al Baghdadi was dead.
Lieutenant General Stephen Townsend said he had heard "all kinds of reporting" about Baghdadi's status.
"I don't have a clue," Townsend said in a video call from Baghdad. "Hope he's deader than a doornail. And if he's not, as soon as we find out where he is he will be.
In June, Russia's defence ministry said it may have killed Baghdadi when one of its air strikes hit a gathering of Daesh commanders on the outskirts of the Syrian city of Raqqa, but Washington said it could not corroborate the death and Western and Iraqi officials have been sceptical.