The Cairo giants have been suffering from below-par signings in the past two seasons in which Zamalek endured trophyless.
"We will not sign any player because he excelled against us like what was usually happening, from now on just the superstars will have a place here," Abbas told a press conference.
"We are fed up with the players who come here just to earn money no matter they are good or bad."
Abbas neither revealed any news regarding the new signings nor wanted to comment about reports linking the club with a move for Anderlecht midfielder Ahmed Hassan.
The Egypt skipper, who will leave the Belgian champions at the end of the season, arrived in Cairo on Thursday amid suggestions that he will negotiate a new deal with Zamalek.
However, Hassan told FilGoal.com earlier that he hasn’t decided yet his next destination.
Abbas apologized to the fans for Zamalek's Arab Champions League elimination at the hands of Jordan's Faisali, but blamed them for their attitude towards goalkeeper Mohamed Abdul-Monsef.
"Insults are not acceptable even if Abdul-Monsef made huge mistakes; I urge the fans to continue their support in a proper manner," he added.