With several teams battling it out to avoid occupying the final relegation place in the Egyptian Premier League, a play-off might be needed to determine who will go down.
Ghazl Mahalla (29 points), Arab Contractors (31 points), Masri (32 points) and Gouna (32 points) are involved in the battle to remain in the top flight with two games remaining.
A possible playoff might further crowd the hectic schedule, fuelling suggestions that the competition committee will have no chance but to cancel the Egyptian Cup.
World governing body FIFA obliged all associations to end the season before the World Cup begins on June 11.
"The Egyptian Cup games will begin right after the end of the league, there is no intention to call the competition off," Barakat told Egyptian radio on Wednesday.
"The cup is an interesting competition for all the teams because winning five games is enough to win the title. It should be held."
The Premier League is due to end on May 17. If two of the relegation-threatened teams finish level on points, a playoff game will take place four days later to separate them.
However, things are not clear as to what will be the solution if more than two teams finish level on points.
"Let's hope that this possibility does not happen. But the Egyptian Cup will go ahead as scheduled in all cases," Barakat added.
Ahli will be looking to win the cup and complete the double after winning their sixth consecutive league title.
Their arch-rivals Zamalek, who enjoyed a huge revival under coach Hossam Hassan, are hoping to salvage their season by clinching the last title remaining this season.
The cup also represents a chance for less glamorous clubs to add to their near-empty trophy cabinet.
Alexandria-based club Harras Hodoud won last season's edition after beating ENPPI on penalties in the final for their first ever trophy.