Hossam Al-Badri resigned as boss after the Red Devils' 3-1 loss at Ismaili in the Egyptian Premier League on Sunday. His resignation was accepted hours later.
Several managers were tipped to succeed the 50-year-old at Ahli's helm, including Mohsen Saleh, Anwar Salama and Mokhtar Mokhtar.
Ahli chairman Hassan Hamdi, vice-president Mahmoud Al-Khatib and Abdul-Hafiz met on Monday to discuss their options, but a final decision is yet to be made.
"We will decide which coach to appoint within 48 hours," former Ahli star Abdul-Hafiz told Ahli TV.
When asked about candidates for the job, Abdul-Hafiz refused to reveal any.
He also refused to rule out the possibility of reinstating Al-Badri.
"A lot of things could happen in the next two days. Al-Badri and his backroom boys (who also resigned) could stay in charge after all," Abdul-Hafiz added.