The under-fire England international was at fault for Chelsea striker Fernando Torres' winning goal in the Premier League encounter at Stamford Bridge last Sunday.
Hart came in for criticism following that costly error and the spotlight was already on the City keeper following mistakes for club and country earlier this season.
Reports on Friday claimed City boss Manuel Pellegrini will replace Hart with Costel Pantilimon when Norwich visit the Etihad Stadium on Saturday.
Romanian Pantilimon started City's League Cup win at Newcastle on Wednesday night and did his chances of being handed a Premier League start no harm by keeping a clean sheet.
Speaking at a press conference on Friday afternoon, Pellegrini refused to be drawn on whether Hart would pay the price for his latest error by being left on the bench against Chris Hughton's side.
"Tomorrow you will know the XI that starts. It's a decision I have to take every week with 22 players." said Pellegrini.
When asked how Hart had taken being left out at St James' Park, Pellegrini added: "You must ask Joe, I can't answer for him how disappointed. All of you saw what happened (against Chelsea)."
Former Malaga coach Pellegrini refused to back Hart following the 2-1 defeat to Chelsea.
The Chilean said: "What do I think about the goal? I won't talk about it. What do I think about my goalkeeper's performance? I repeat, the analysis I do with individual players I do with the players."
But midfielder Jack Rodwell had some words of support for his City and England team-mate.
"Joe is number one and Costel is good competition for him," he said.
"We all know Joe is number one but Costel put on a good performance against Newcastle.
"He's an international goalkeeper but having Joe in front of you would be difficult for a lot of keepers.
"He digs away, puts on a good performance and the Capital One Cup is good for him this season.
"He made two saves which kept us level - if they had gone in, the tie could have gone either way.
"He's a good lad who trains every day. He and Richard Wright (third choice goalkeeper) are both good."
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