Hart's form is again under scrutiny after two errors in City's 3-1 Champions League hammering by Bayern Munich at the Etihad Stadium on Wednesday night.
The England number one failed to keep out a saveable Franck Ribery shot for the Germans' opener and was beaten too easily at his near post by Arjen Robben for the European champions' third.
There were the latest in a growing series of mistakes by Hart in an indifferent run now stretching back almost a year.
When asked if Hart could be dropped for City's home game against Everton in the Premier League this weekend, Pellegrini was equivocal.
Pellegrini said: "I will decide on Saturday if he starts. I don't tell you now if Joe will play because the players don't know yet.
"Of course Joe knows he must improve the way he is playing but he has our trust."
When asked further Pellegrini, speaking at his pre-Everton press conference, said: "I am always contemplating different things. I will decide."
Hart has received the full support of England manager Roy Hodgson, who has said the keeper will play in the vital upcoming World Cup qualifiers against Montenegro and Poland.
Pellegrini is also supportive and is confident the 26-year-old will bounce back.
He said: "Of course, he feels that he didn't do very well but I think he doesn't have any problem.
"He continues with the trust of all the team and with our trust so we hope he will recover soon from what he did last match."
One of the criticisms leveled at both City and England is that there is a lack of serious competition for the goalkeeper's jersey.
From City's point of view, Pellegrini does not agree, insisting Romanian Costel Pantilimon is a viable alternative.
He said: "Costel Pantilimon is a very good goalkeeper also, he has all the rights to play.
"He is working hard and I am absolutely sure, if it is Saturday or another game and he must play, he will do well."
I've said it for years, Joe Hart is not good enough, watch the way he chews his gum when standing in the sticks, it's like he thinks he's the best in the world, when he concedes he often smiles about it, other goalkeepers look gutted, but not our Joe here. He makes more errors than any other goalkeeper, having a good goalkeeper is important in terms of goals conceded at the end of the season and Joe is letting in at least 7 or 8 that could have been saved per season.- dannyjohnson