England's first-choice keeper has been left out of City's opening three Premier League matches of the season and new manager Pep Guardiola has said that Hart can leave if he wants.
Guardiola is determined to start moves at the back with a goalkeeper who is "able to play with the ball".
City and Torino are discussing Hart's possible loan move, according to media reports.
Torino sporting director Gianluca Petrachi was quoted as saying: "The goalkeeper is an idea we wanted to follow.
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"If it's Hart then good, otherwise we will certainly be doing something on the market for that role."
Torino, who finished 12th in the league last season, have started the new campaign by taking three points from their first two games.
(Writing by Tony Jimenez; Editing by Clare Fallon)
