His death, reported by the respected Turkish daily Yenis Safak, would be a major blow for the jihadists and comes only days after 50 people were killed in an Orlando nightclub by a man pledging allegiance to ISIS.
But there have previously been reports that al-Baghdadi, who proclaimed himself caliph of all Muslims two years ago, has been killed or wounded.
The Abna24 website said al-Baghdadi had been killed on Sunday morning by an air strike in Syria but the US-led coalition has made no comment.
But there has been no confirmation from the US or any other coalition powers.
A Pentagon spokesman told Mail Online they were not aware of any ‘high value targets’ having been killed.
He was born as Ibrahim Awwad Ibrahimal-Badri, in 1971 in Samarra, Iraq, to a lower-middle class Sunni family.
His tribe claimed to be descended from the Prophet Muhammad.
As a youth Baghdadi was a meticulous observer of religious law and could recite the Koran from cover to cover.