The England number one did not feature in the Capital One Cup fourth-round tie at Newcastle in midweek but it remains to be seen whether his costly error against Chelsea last weekend will lead to him forfeiting his place in the Blues' Barclays Premier League line-up as well.
Asked if Hart would play against Norwich, the Chilean said: "Tomorrow you will know the answer."
Various commentators have had their say on Hart's form and Pellegrini must decide whether dropping him will protect him from the limelight or further knock his confidence.
Asked whether it was a difficult decision, he added: "It is a decision I have to take every week with 22 players of the team."
Costel Pantilimon played ahead of Hart on Wednesday night and the Blues boss would not be drawn on how the Englishman had reacted to that decision.
"You must ask Joe - I can't answer for him how disappointed he was," Pellegrini said.
"All of you and the players and me all saw what happened. But he is a football player and every week he is under the same pressure.
"I am always careful with all the players, not only Joe."