Richards - who plays for City against Blackburn at home tonight - has been offered a deal to make him one of the club's highest-paid players and will take home £50,000 a week if he agrees to stay.
City manager Sven Goran Eriksson said: "I am not sure how close Micah is to signing but I know that he will sign. I have spoken to him and he is very happy at this club.
"We would like him to stay here for the rest of his career if possible. There is no reason why that shouldn't happen and we have offered him something that reflects how highly we value him."