Holders Ahly were handed a stiff group in Saturday's African Champions League draw alongside JS
Kabylie of Algeria, Tunisia's CS Sfaxien and Ghana's Asante Kotoko.
Ahly play in group A of the league phase of the competition, which has had its start postponed from later this month to 14-16 July.
The Confederation of African Football said it was postponing the start because Asante Kotoko and Hearts of Oak have players in the Ghana squad for the World Cup finals in Germany.
Ahly start their campaign away at CS Sfaxien on 15 July.
Four former winners were drawn in Group B with Enyimba of Nigeria favourites ahead of Hearts of Oak, ASEC Abidjan of the Ivory Coast and the South African side Orlando Pirates.
Enyimba have an away game in their first group match at Hearts of Oak on 16 July.
The top two finishers in each group go through to the semi-finals in October.
The final is scheduled to be completed by 12 November.