The Egyptian international joined Anderlecht on loan in the summer from Ahly and has so far failed to establish himself, playing only 140 minutes in six games.
"Anderlecht sent us an official letter asking to sign Trezeguet permanently," Ahly said in a statement via its official website.
"The Belgian club confirmed they will be fully committed to the terms of the loan contract," added the statement without referring to a date for the club's reply.
Late in March, Trezeguet announced that he won't leave Anderlecht as he is still searching for a regular place in the team's starting lineup despite that his loan deal is close to expiring.
After his recovery from a shoulder injury during an Egypt training camp in October, 'Trezeguet' has struggled to clinch a starting role with Anderlecht.
The 22-year-old winger refused to criticise Anderlecht's coach Besnik Hasi for not naming him in the team's squad during the Belgian league games despite the season being close to finishing.
"I will not criticise Besnik Hasi. He is an experienced coach and knows what he's doing," Trezeguet said during an interview with anderlecht-online in March.
"I'm ready to help the team but if the coach asked to wait I will wait as I have a strong mentality and patience," he said.
"I won't repeat the other Egyptian players' mistakes who left their teams for not participating and who terminated their contracts with European teams."
"I'm happy to stay at Anderlecht and I thank Mr. Van Holsbeeck for his confidence in keeping me in the team's squad," the Egyptian winger added.
"I convinced him that I will succeed in Anderlecht. I have a dream, and that is to play in the biggest club in the world like Real Madrid."
"I know that if I returned to Egypt, my European dream will be over," Trezeguet concluded.
Despite a lack of game time, Trezeguet was part of Egypt's national team squad that defeated Nigeria in the African Cup of Nations qualifiers last March.
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