The 60-year-old coach led Egypt to this year's World Cup round of 16 where they squandered a two-goal lead in a 3-2 defeat by eventual finalists Argentina.
Under Hassan's management, Egypt secured their first World Cup win by beating New Zealand.
Egypt also reached the semi-finals of the 2025 Africa Cup of Nations.
Hassan, who was appointed in 2024, said in June that he had been working without a contract since February 2026.
Egypt will face Angola and South Sudan on September 25 and 29 in the 2027 Africa Cup of Nations qualifiers.