The source said that al-Baghdadi left Rawa for Syria's Deir Ezzur along with a number of ISIL commanders after the Iraqi forces captured the town of al-Qa'em.
The source added that al-Baghdadi called on ISIL fighters in al-Qa'em to continue battle with Iraqi forces, but, he himself escaped from Rawa.
The source who requested to remain anonymous said that al-Baghdadi left Iraq for Syria in a yellow taxi and would be in Deir Ezzur province.
The report comes as there have been contradictory reports on the fate of Baghdadi putting his life or dead under a question mark.
The Iraqi forces managed to capture al-Qa'em near the Syrian border from the ISIL group on Friday.
"Army troops backed by Hashd al-Shaabi fighters and Arab tribal volunteers have completely liberated the town of al-Qa'em’s center,” Colonel Walid al-Duleimi said.
"The Iraqi national flag has been raised over the town’s local government headquarters,” he added.
The commander stressed that Iraqi forces also established control over the nearby al-Qa'em border crossing.
Also, Prime Minister Haider al-Abadi announced that Iraqi forces retook control of the town of al-Qa'em from ISIL terrorists, congratulating the troops on their latest victory against the terrorist group.