The Japan international has been at the San Siro since 2011 and he has impressed during his time there.
Inter have recently offered the 31-year-old a new contract, with his current deal due to expire in June 2019.
Nagatomo is now mulling over that proposal as he is considering trying a new challenge elsewhere.
And if the left-back does decide to leave Inter, according to Tuttomercato, Burnley, Newcastle and West Brom are all ready to pounce.
The Premier League trio are reportedly tracking Nagatomo and they are willing to firm up their interest if a deal looks on the cards.