Hart has been under intense pressure this season because of a number of high-profile mistakes, the latest of which came in City's Premier League loss to Chelsea at the weekend.
Romanian Costel Pantilimon, a cup regular, was given the nod for Wednesday night's Capital One Cup tie against Newcastle and kept a clean sheet, and Pellegrini refused to confirm whether Hart would return for the Premier League clash with Norwich on Saturday.
Friedel helped Tottenham reach the League Cup quarter-finals with a penalty shoot-out victory over Hull, and he told talkSPORT: "All goalkeepers go through ups and down.
"Goalkeeping is very much a confidence position. Joe has never struck me as a person who lacks in the confidence department.
"The manager has a decision to make and he's the only one who knows how Joe's performing day in, day out in training. If he feels he's performing well, he'll stick with him. If he feels he needs a rest, he'll put the other fellow in.
"Being dropped can have a positive effect, but that depends how you take being dropped. If you sulk and stop doing your work, it's going to have an adverse effect. If you knuckle down and work even harder and take your chance when you get in again, it can have a positive effect.
"You just never know with these things. That's why it's not as easy as, 'Right, we're going to drop Joe Hart', because you don't want to lose the best Joe Hart, because the best Joe Hart is England's number one."
Speaking after the cup win over Newcastle, Pellegrini said: "I will start to think about the game against Norwich on Thursday.
''One goalkeeper can play but the other will have our full support. We will think about it.
"(Pantilimon) is a good player and is not playing too much because Joe Hart played this year and last year, but I trust him and for him and for the whole team to keep a clean sheet after six games is very important.''