Esperance president Hamdi Meddeb has also finalized an agreement with the defender and only minor details need to be sorted out before confirming the move, according to the Tunisian paper.
The Tunisian international joined Zamalek from Sfaxien in January 2006 and had a bright start for the Cairo giants, establishing himself as a regular first-team player.
However, El-Abdi's relationship with Zamalek officials has seemingly reached a dead end after being sent-off in the 1-1 draw with Suez Cement for an ugly lunge on Mohamed Al-Saghir.
Reports said El-Abdi deliberately hit his opponent to fly to his homeland for a vacation, but the 25-year-old firmly denied the allegations.
It remains to be seen whether El-Abdi will have another chance to play for the men in white.