Toure, 34, is out of contract next month and is mulling over new terms to remain for next season.
City chief Khaldoon Al Mubarak hopes the midfield star will sign a new deal because he has proved his value to the team during his seven years with the club.
“Yaya has shown us this year again and again how he can contribute to this team,” said the Blues chairman.
“This year has been another year in which he has shown us on the pitch the type of player he is, the type of personality he is, and how he continues to be a player who can give to the is team and to our organisation.
“Pep, as you have seen obviously this year, has a lot of trust and confidence in him.
“So Yaya I hope will be with us and continue his journey with us.”
Al Mubarak also claims City want to keep star striker Sergio Aguero – because he is key to their hopes of winning silverware.
“Sergio Aguero is one of the best players in the world. And we are a team that aspires to win in every competition we compete in.
“Having Sergio Aguero part for the squad is an absolute must. And it has never been in doubt.”