Toure has been leading the Sky Blues in Kompany's absence, and Pellegrini's decision to demote Zabaleta is said to have caused friction in the dressing room.
"Some of the players are surprised and disappointed that Pablo has been stripped of the vice-captaincy," a purported inside source told the Daily Star.
"Pablo is the ultimate professional. He is so influential on the pitch and in the dressing room that there was a sense of shock at that.
"He has worked with the manager before so the assumption among the group was that Pablo would continue to wear the armband in Kompany's absence."