City have collected a perfect 21 points since Hart's return seven games ago - but the keeper has been told in no uncertain terms that he must not allow his performance level to drop.
"It is very difficult to talk about the future," said Pellegrini when asked Hart has proved himself to be his long-term No.1.
"All that matters is the present. Of course I trust Joe Hart because I see him every day when I work with him.
"I think Hart has improved a lot. It was very important for him to have a rest and now he is showing good performances. That's very important to us.
"He was not taking good decisions at that moment and maybe his was not 100 percent.
"But all that matters is the present.
"For the players and especially the manager, all that matters at this moment is the next performance and result."