Darmian, formerly of Torino, could be headed for Italy before the European transfer window closes on September 2. Meanwhile, centre-back Marcos Rojo, who came close to a Deadline Day move to Everton, will be staying at the club.
"I can see maybe Matteo [leaving]. There has been some interest in Matteo over in Italy, wanting to go back home," said the United boss.
"Marcos is staying definitely so we have a squad now that's less in numbers but still big enough and strong enough to have coverage in all positions."