"We have successfully concluded negotiations with Fathallah," Refaat told FilGoal.com.
"He will pen a contract extension within the coming few days," the Zamalek icon added without disclosing the details of the new deal.
Fathallah was apparently reluctant to prolong his stay beyond the end of the season when his current deal expires.
He fuelled speculation that he might make a shock move to Zamalek's arch-rivals Ahli, who said they would be interested in signing him 'if he was available'.
His decision to stay put will come as a major boost for a Zamalek side which are beset by uncertainty surrounding the future of some key players.
The White Knights are also looking to convince Fathallah's defensive partner Hani Saied and midfielder Hassan Mostafa to put pen-to-paper on new deals.
"We are on the verge of closing this chapter," Refaat, a member of Zamalek's interim board of directors, concluded.
Fathallah, who joined Zamalek from Ghazl Mahalla in 2007, is one of the team's consistent performers although their defense has been shaky so far this season.
The Cairo giants lie second in the league table but they leaked 10 goals in their first seven games of the competition.
Fathallah, 28, was part of Egypt's African Cup of Nations winning squads in 2008 and 2010.