The Wales international has been a regular since making the move from Swansea City in 2019, clocking up 72 appearances over the last two seasons.
The 23-year-old winger only featured on 15 occasions in the English top flight last term, though, and the arrival of Jadon Sancho has seemingly pushed him further down the pecking order.
According to Tuttomercatoweb, Atalanta are interested in signing James and could launch a bid for his services before the transfer deadline.
The Welshman still has three years left on his contract at Old Trafford.
James has contributed six goals and seven assists in 48 Premier League appearances.