"Zaki is not for sale. We need him to help Zamalek break their title drought," Abbas told the club's website.
"The price offered does not suit someone of Zaki's caliber."
The prolific striker has persistently asked for a move abroad and claimed more than once that he had several offers from Premiership sides.
But Zamalek insisted there hasn't been any official approach. It is the first time the club admit receiving an offer for Zaki.
Wigan apparently need reinforcements in January as they struggle in the Premiership table, sitting second from bottom on just nine points.
Zaki Problems
Since his arrival from Lokomotiv Moscow in the summer of 2006, Zaki has been involved in many disputes with the club's board, teammates and coaches.
He missed two months this season after being banned for publicly criticizing his teammates before being involved in an altercation with assistant coach Ayman Mansour.
Zamalek fans even attacked the 24-year-old when he came on as a second-half substitute in the team's 3-0 victory over Tersana on Friday.
However, Zamalek opted to keep Zaki despite his desperate attempts to depart the five-time African champions.