The Spurs star is believed to be looking to leave White Hart Lane in the coming months in search of Champions League football, which has alerted Manuel Pellegrini.
Although he has reinstated Hart after placing him in first-team exile earlier this season, the City boss is rumoured to remain unconvinced as to whether or not the England international is the right man to possess his side’s number one jersey.
Lloris on the other hand is a stopper that he is thought to see as a ready-made first choice, following the Frenchman’s fine displays for the London club.
In order to lure him to the Etihad Stadium, Pellegrini is understood to be ready to let Hart move in the opposite direction.
Lloris is liable to be open to such a switch with City certain to be able to offer him top level European football over the coming seasons, yet the current Sky Blues star may be more reluctant to join the Lilywhites for the reverse reason.