The Red Devils' habitual success this season could turn into a more remarkable one if they managed to win Egypt's secondary competition.
They eased to a 3-0 victory over second-division side Nabaroh to book a last-16 berth but a much sterner test awaits them.
They will face arch-rivals and league runners-up Zamalek, whom they failed to overcome in two league meetings this term.
Their first clash ended goalless while Ahli needed a last-gasp strike from Mohamed Barakat to earn a 3-3 draw in the second last month.
"Our game against Zamalek is very important," Al-Badri said on Ahli's official website on Monday.
"Beating them will help us edge closer to achieving our last target this season, winning the Egyptian Cup to complete the double.
"I'm watching several games for Zamalek to assess their displays and be fully ready for the game."
Al-Badri is beginning to win over Ahli fans after a slow start prompted them to recall the glory days of coach Manuel Jose, who left the club last summer.
A victory over Zamalek will further prove that Al-Badri, who signed a one-year contract extension last week, was the ideal replacement for the Portuguese tactician.
"I'm sure our fans will strongly support us against Zamalek. We want to do our best and win more trophies for their sake," the 50-year-old added.
Ahli, who eye a 36th cup title, last won the double in 2007 after beating Zamalek 4-3 in a memorable Egyptian Cup final.