Board members Ibrahim Youssef and Hazem Emam have been assigned to negotiate with the former Egypt hitman over the new deal.
"We unanimously want to renew Hassan's contract for the sake of the team," Youssef told FilGoal.com.
"The promising results and Zamalek's current status in the league table urged us to make this decision."
Zamalek suffered a terrible form and a string of poor results under Swiss tactician Michel Decastal and Frenchman Henri Michel early this season.
However, the Cairo giants have shown a great deal of consistency since Hassan took the helm late in November, after both of his predecessors were sacked.
Now Zamalek, who lie fifth in the Egyptian Premier League table, revel in a six-match winning streak.
The White Knights were languishing in 10th spot near the relegation zone by the time Hassan was appointed as tactician.
"A meeting with Hossam and his backroom boys is due to be held in the immediate future," Youssef, a former Zamalek defender, added.
"We will probably sit down after Zamalek's friendly game with Mansoura on March 2nd."