Hart has returned to City after a mixed loan period with West Ham United, but the England worldwide is expected to leave the Etihad Stadium before the end of the transfer window.
Pep Guardiola was forced to field a makeshift line-up with plenty of youngsters and players who spent last season out on loan, with 16 senior players still to join up for preseason after playing at the World Cup.
First team stars such as Kevin De Bruyne, Sergio Aguero, Vincent Kompany, Ederson, David Silva, Gabriel Jesus, Raheem Sterling, Kyle Walker and John Stones have not made the journey to compete in the annual International Champions Cup pre-season tournament with most not expected back until a week before the start of the domestic season in England.
When Guardiola was asked about Hart on Friday at a press conference in Chicago, he said: "Joe is our player, so in that situation he is here and we are going to try (to find) a solution for him, for the best for him". He's training like a young guy of 18 years old.
Also in the squad is City's summer signing Riyad Mahrez, the winger recruited for a club-record fee of £60million from Leicester.
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Jorginho was tipped to make the move to City, however, the Italy global midfielder opted to reunite with former Napoli boss Maurizio Sarri at Chelsea. "If not, he will stay here", Guardiola said.
"It would have been a mistake for him if he came and he wanted to go to Chelsea with (new manager) Maurizio Sarri".
He was one of Dortmund's brighter players and has been praised by head coach Lucien Favre, who described him as "an extremely good player" with "exceptional potential".
"Leroy has to accept that this decision may make him stronger".