The club completed the £13.75m signing of keeper Claudio Bravo from Barcelona on Thursday.
They now have Bravo, Willy Caballero, Hart and highly-rated youngster Angus Gunn.
It means England No 1 Hart is now effectively City’s third choice keeper as his 10-year career at the club looks like ending on a huge low.
Boss Pep Guardiola has told Hart he will be part of the rotation for the spot on the bench if he does not find a new club by Wednesday night when the transfer window closes.
Hart is desperate for a move but has been left in limbo with little interest and his wages thought to be a stumbling block.