The England goalkeeper has come under fire following a mix-up which gave Chelsea a late winner during their 2-1 win over City last Sunday.
McLeish, who managed Hart during his loan spell with Birmingham City during the 2009-10 season, told Sky Sports News: "I do believe that Joe will get over this. We don't know what's going to happen tomorrow. Speculation is that [Manuel] Pellegrini might leave him out.
"[Costel] Pantilimon did really well the other night, made a great point-blank save at 0-0, took cross balls well, but I'm sure Joe will be bursting just to show everybody he can do it. Whether he gets a reprieve from Pellegrini remains to be seen.
"Certainly [England manager] Roy [Hodgson], in a team such as England's magnitude in world football, they wouldn't go, I don't think they would go, with a goalkeeper who's been out of his club football for a long period of time."
City face Norwich City tomorrow afternoon.