Reports in Ghana linked Ayew, the son of three-time African Footballer of the Year Abedi 'Pele', with a European move.
"I did not receive any offers. I want to continue playing with Zamalek until the end of the season because they are a very popular team who can help me play in the World Cup," Ayew told FilGoal.com.
"My presence in Zamalek's squad has already helped me play in the African Cup of Nations, so I wish to remain with them."
Ayew has been used mainly as a substitute since his summer arrival but his versatility gives the Cairo club plenty of options.
He is not a regular member of Ghana's starting line-up either but was used on several occasions as a left-back during the Nations Cup.
The 24-year-old did not play in the Black Stars' 1-0 defeat to champions Egypt in the tournament's final.
Four-time African champions Ghana were drawn with Germany, Australia and Serbia in Group D of the World Cup, which will take place in South Africa.
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Zamalek give Ayew chance to play in World Cup