The England goalkeeper was benched for City's first two Premier League games of the season, with Guardiola preferring Willy Caballero to the 29-year-old.
And with the signing of Caludio Bravo, Hart is expected to become City's third-choice goalkeeper and is free to look for a new club.
Both Borussia Dortmund and Sevilla have been linked with Hart, but now AC Milan and Torino are allegedly interested in taking the player on a season-long loan.
The 'Sunday Express' is reporting that the two Serie A clubs want Hart, whose wages will partly be paid by Manchester City.
AC Milan will be hoping to get back to the top of Italian football while Torino will be looking to improve on last season's 12th-placed finish.