The right-back has been linked with both Premier League giants as they look to strengthen their defences over the summer months.
Tuttosport reports that City have made a €60 million bid for the Portugal international, which will be hard for the Turin club to resist having signed him from Valencia for just over €40 million last summer.
However, a decision must be made on who will succeed Massimiliano Allegri on the Old Lady bench before a move goes ahead.
Chelsea boss Maurizio Sarri is the leading candidate to take over at the Italian champions as things stand.
Once a new coach is announced, the club will look to sell Cancelo in order to raise funds for the transfer window.
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