Allardyce insists that Hart, who has been dropped by new City coach Pep Guardiola, will be included when he names his first England squad on Sunday, but added that his continued presence on the bench might harm his chances of remaining the Three Lions No1.
“The problem for any player you want to select for England is that it will be a concern if a player doesn’t play for his team,” he said.
“He will be in the squad, definitely. What do we do [regarding selection]? I won’t really know that until I speak to Joe and that will be the same with most of the players when they arrive.”
Hart, who faces competition for the No1 shirt from Southampton’s Fraser Forster, has been linked with loan moves to Everton, Sevilla and Borussia Dortmund.
Allardyce has also remained non-committal on whether Wayne Rooney will retain the captaincy when he takes charge of his first game, a World Cup qualifier in Slovakia on 4 September.
He added: “We’ll meet up [next week] and the first thing I would probably choose to tell the public and the media would be who is going to be the captain so we can get that one out of the way.”