Hart has come under criticism for a mistake that resulted in City losing to Chelsea last weekend, and with Costel Pantilimon waiting in the wings, Pellegrini has a decision to make ahead of Saturday's game.
However, when asked about who would get the nod against the Canaries, the Chilean has insisted that his selection would not be made public until an hour prior to kickoff.
The 60-year-old told reporters: "Tomorrow you will know the answer. It is a decision that I have to take every week with 22 players of the team."
City have won each of their four Premier League games at the Etihad Stadium this season.