Mike McGrath of The Sun (h/t MailOnline's Danny Gallagher) reported the defender is set to depart Old Trafford if the Red Devils can negotiate a suitable price. United have an optional one-year extension to trigger in the player's current deal but will consider offers for his services in January.
The 28-year-old made a promising start to life at the Theatre of Dreams three years ago, but he's failed to hold down a starting role since a £12.9 million switch from Torino.
Former coach Louis van Gaal appeared to have faith in the Italian, but current manager Jose Mourinho has used the player sparingly.
Antonio Valencia has remained United's primary right-back in recent years, but Diogo Dalot is expected to be given the role after he fully acclimatises to life at Carrington. The teenager was signed from Porto last summer but is yet to make a consistent breakthrough.
Darmian recently admitted he wants regular football and is ready to return to his homeland if he gets the opportunity.
Speaking to Italian newspaper Libero (h/t Calciomercato), Darmian said:
"United is one of the biggest clubs in the world, anyone must deserve the place and I work in light of this.
"But of course I'd rather play more, even if it means leaving Manchester; where I dream of going back to is Italy, in Serie A, where I got a lot of satisfaction."
The player has started just one game in the Premier League this season and was found wanting in the match at home to Leicester City.
Football writer Liam Canning was far from impressed by Darmian's display:
Darmian's lack of quality in advanced positions has seen him become a limited asset for Mourinho.
The defender doesn't have the ability to pass his opposing defender, and he prefers to play a more static game in the back four.
Dalot's arrival was the true ending of Darmian's long-term chances at United, and Serie A is an appropriate destination for the right-back.
The player has the experience to feature for big teams such as Inter or Roma, and he would fit perfectly in either squad once the winter transfer window opens for business.