The Pharaohs are reeling after suffering a shock 1-0 defeat at tiny Niger in the African Cup of Nations qualifiers on Sunday.
A stumble against Jordan could undermine the confidence of Egypt players, the Egyptian FA believes.
"We don't want anything to further affect the morale of the players," an EFA source, who spoke on condition of anonymity, told FilGoal.com on Wednesday.
Zamalek coach Hossam Hassan has recently called on the EFA to cancel the Jordan game.
He said he would not have sufficient time to prepare his players for Zamalek's anticipated Egyptian Premier League clash against leaders and surprise package Police Union.
Zamalek's match against Police will be played on October 26, just four days after Egypt face Jordan away from home.