The Masri duo have accepted Zamalek's offer but they are waiting for president Sayed Metwali to return to Egypt in order to finalize the deal.
Al-Safti's contract runs out at the end of the next season while Zekri still has two years to fulfill.
Both of them will earn EGP 450,000 per season, to be increased with EGP 50,000 each season.
Meanwhile, Zamalek said they are interested in signing Ismaili duo Moatasem Salem and Youssef Gamal.
Zamalek president Mortada Mansour will hold a meeting with his Ismaili counterpart Yehia Al-Koumi on Saturday to discuss the financial details of the transfer, Filgoal.com correspondent in Ismailia city learnt.
Zamalek are looking to make up for a disappointing two successive seasons in which they failed to win a single trophy, the Egyptian Cup is their last chance to earn silverware this season.
Reports suggested that Ismaili will ask for a swap of their duo for Mohamed Abdul-Monsef, Wael Al-Qabani, Mohamed Abdul-Wahed, Mahmoud Mahmoud and Ahmed Bakri.
Ismaili coach Theo Buecker wants to add trio Abdul-Monsef, Al-Qabani and Abdul-Wahed to his ranks for next season.