The 24-year-old has been with the Turin club since 2022 when he signed from Genoa.
However, BBC states that there is a willingness from all parties to get a deal done.
City are eager to bring in the left-back as soon as possible, due to a lack of options in that position.
The Italy international, who can also fill in at right-back, is the style of player City boss Pep Guardiola prefers.
He is good with his feet and can step into midfield, but has the physical presence to be in the backline.