The head of the Islamic State Libyan faction is most likely to become the new ISIL leader, said a report by Saudi TV station Al Arabiya.
Jalaluddin al-Tunisi had been very close to the ISIL head Abu Bakr al-Baghdadi, who was reportedly killed in a Russian airstrike in Syria.
ISIL has confirmed his death and said the name of a new leader would be announced soon.
Analysts say the terror group is seeking to survive and even expand in North Africa after its losses in Iraq and Syria.
Saudi television's report came a day after Iraqi Prime Minister Haider al-Abadi formally declared Mosul liberated from ISIL after nearly nine months of fierce fighting.
Related story: