Hart is under pressure after a poor start to the season.
Pellegrini said: "I saw the whole of last season, but last season is past. We must see about the present and future and for this moment, I think it is best for the team that Joe Hart continues.
"Joe is working with another goalkeeping coach. I trust a lot in Xabier Mancisidor, he is a very good goalkeeping coach. I worked a lot with him in Malaga and Real Madrid and I am sure Joe will improve in a lot of things during the whole year.
"Joe is a very young goalkeeper, I think he arrived to the top in England maybe too young and he needs a lot of things to improve and Xabier will do it."
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