The Italy international played in both full-back positions last season and started the Europa League final against Ajax.
The right-back has been strongly linked with a return to Italy after starting just 15 Premier League games last season.
United's first-team squad has been split into three groups during the transfer window.
Manchester United manager Jose Mourinho is reportedly keen on keeping versatile full-back Matteo Darmian at the club this summer against a backdrop of persistent speculation linking the player with a move away from Old Trafford after only two seasons.
Tsonga sans trembler, Herbert profite de l'abandon de Kyrgios
Le 10e mondial, qui disputait sa 150ème rencontre en Grand Chelem, n'a eu besoin que de trois sets (6-3, 6-3, 6-2) pour accéder au deuxième tour.
Darmian will need to be playing regularly next season if he wants to be part of Italy's squad for the 2018 World Cup in Russia.
But Mourinho would prefer to keep things as they are, with the Portuguese tactician instead focused on landing a new striker, winger and central midfielder after already splashing the cash on Victor Lindelof. Marcus Rashford and Eric Bailly are given as examples of those in another group who will not be sold for any price, while there is a third group featuring the likes of Adnan Januzaj that the club is actively looking to move on.
Mourinho does hold an interest in Barcelona left-back Jordi Alba, but the Spain international looks set to stay at the La Liga club.
Darmian was initially considered as a backup to Antonio Valencia in the right-back role, however, he made the majority of his 29 appearances at left-back whilst Luke Shaw and Marcos Rojo picked up injuries.
- Danone cède Stonyfield à Lactalis pour 875 millions de dollars
- Arrestation d'un homme qui projetait de tuer des migrants — Bouches-du-Rhône
- Bank of England facing first strike from workers in 50 years
- 'Fantastic Beasts' sequel begins filming, new characters and plot revealed
- BAE Systems share price: Group lands £3.7bn Royal Navy deal
- Activision Blizzard, Inc (NASDAQ:ATVI) Shares Sold by Mackenzie Financial Corp
- LG unwraps G Pad IV 8.0 FHD LTE Tablet in Korea
- Ces joueurs d’origine africaine évoluant pour des nations européennes
- Pope calls for end to Venezuela violence, prays for victims
- Harrison Lake fire not yet under control