However, the 64-year-old Three Lions boss has kept faith with the struggling keeper for the upcoming friendlies against Chile and Germany, one of which he will start.
"I certainly don't intend to have a rule that if you don't play for your club side you don't play for England," The Telegraph quotes Hodgson as saying. "I would never go that far, but on the other hand, I'm not prepared to say: 'If you are not in your club side don't worry you will be in with England.'
"Joe's only lost his place one game ago because we can forget about the Champions League game that City were going to win at a canter anyway. So that might be a more relevant consideration for me in March or February if he goes three months and has been replaced and never gets a game.
"I would have to cross that bridge if I come to it. For the moment, I'm selecting a squad for Chile and Germany and the keeper I think is the number one has been dropped for the one, possibly two, matches before it. But I am still picking him."
City take on Sunderland at the Stadium of Light this afternoon.