The 29-year-old joined the Turkish giants in the summer from Swansea City on a long season loan with an option of making the deal permanent.
The former West Ham attacker have shown his qualities on the pitch and have scored two goals in the ongoing campaign.
“I have one request, I want you to become the leader of the team. Everyone respects you,” Fotomac quoted Cocu as he told Ayew.
“You will play various offensive roles also on the field,”
Cocu’s comments could see first-choice goalkeeper Volkan Demirel losing his role as the captain of the side.
Andre Ayew captained Ghana’s U20 team to win the 2009 FIFA World Youth Championship in Egypt.