Iraqi forces have reportedly launched an offensive to capture the last town under Islamic State (IS, formerly ISIS/ISIL) control - the town of Rawa.
The military unit did not say what had happened to Baghdadi, give further details or identify its sources. The report did not elaborate on how the soldiers heard about al-Baghdadi or what they were doing about the information.
The recapture of the Rawa pocket would mark the final battleground defeat of IS in Iraq and sound the death knell of the sprawling "caliphate" the group declared in 2014 over a swathe of Iraq and Syria the size of Britain.
For instance, the SDF took control of the Abu Omar oil field - the largest in all of Deir Ezzor - last month after ISIS militants defected to the SDF.
Syrian regime forces and allied militia overran Albu Kamal, which lies on the border with Iraq, on Thursday but have since faced a string of IS counter-attacks.
The Observatory also reported 26 civilians killed, including nine children, since Friday night in artillery fire by government forces and Russian air strikes that hit villages and camps for those displaced by the fighting in Albu Kamal.
Two infantry divisions and Sunni tribal forces are participating in the offensive to recapture Rawa, a small town on the bank of the Euphrates, and its surrounding areas along the border with Syria.
Abu Kamal is the main border crossing into Iraq, where it links with al-Qaim, another town which recently fell to Iraqi forces from ISIS.