The Italian is keen on a return to his homeland this summer, with the likes of Juventus, Napoli and Inter Milan having all been credited with holding an interest in the versatile defenders.
Darmian played the full 90 minutes of United's 2-1 victory over Leicester City in the season opener on Friday, but is likely to slip down the pecking order significantly as and when Antonio Valencia and Diogo Dalot return to full fitness.
United boss Jose Mourinho has admitted that the club will cash in on Darmian if the price is right, with the club believed to be hopeful of recouping the £13m they paid torino for his services back in 2015.
"Matteo wants to leave," Mourinho admitted last month. "If the right offer arrives you have to try to be human and let the player follow his instinct but not at any price."
According to the 'Manchester Evening News', the Italy international is currently staying at a hotel in Manchester as he prepares to leave the club, with his wife having remained in Italy following their holidays.
Serie A sides have until August 31 to complete any remaining transfer business.