Hart has been City and England's undisputed number one for the past few seasons.
He was beaten three times against Cardiff City last week, and his manager has insisted that his place in the side is not guaranteed.
"For the moment Joe will continue being our goalkeeper," Pellegrini told reporters. "I spoke with him and he knows he must be on top form again quickly.
"I said from the beginning, my teams never play with names, they play with performance. Joe knows he needs good performances in the next games.
"Joe is a young goalkeeper. He reached the top in England maybe too young and he needs a lot of things to improve. [Goalkeeping coach Xabi Mancisidor] will do it."
Hart is in goal for City's game against Hull City this afternoon.