The central defender, a key member of Zamalek's starting line up, has yet to extend his contract, which will expire at the end of the season.
The club said they were puzzled as to why Fathallah is stalling on the new agreement although they fulfilled his financial requirements.
"I'm dismayed by Fathallah's attitude. He suddenly backtracked on his initial decision to sign a new deal although we were ready to give him the money he wanted," Hossam Hassan told FilGoal.com.
"I can't find suitable words to describe my disappointment with the player's attitude. We want to keep hold of him but he seemingly has another point of view."
Fathallah said he was awaiting an offer from a Gulf club but widespread reports suggested that Zamalek's arch-rivals Ahli were lining up a move for the Egyptian international.
Fathallah would be a major swoop for the Red Devils, given their shortage of options in central defense.
"I tried to advice him and make it clear that he might lose the support of Zamalek fans, who greatly love him," Hassan added.
"Fathallah should now tell those fans why he is refusing to sign a new deal."
The 28-year-old, who is known for his aerial prowess, usually partners Amr Al-Safti in the heart of the White Knights' defense.
He is the team's second-highest scorer with four goals, four behind in-form forward Shikabala.