Hart has found himself on the sidelines since being left out of the side in October following a string of high-profile errors, with Romanian keeper Costel Pantilimon being Pellegrini's preferred choice.
However, the England number one is set for a return to the starting lineup against Bayern Munich on Tuesday, and Pellegrini believes that it is a "very important" match for the 26-year-old.
"For him it is a very important game. I am not thinking about the past, just thinking about the future. I trust in him," Pellegrini told reporters.
"I don't think this press conference is for talking about Joe Hart. I have said in other weeks what I think about him and his performances. Today is not the day to analyse this."
Should Hart face the reigning European champions, then it would be just his second appearance in City's last 10 matches.