The 20-year-old has only played for Ole Gunnar Solskjaer’s United five times this season as the summer signing of Alex Telles has limited the England U21 international’s playing time.
Williams’ sole Premier League appearance was as a late substitute in United’s 3-2 win over Southampton.
By comparison, Williams featured for the Red Devils on 36 occasions in all competitions last season.
Sky Sports say Williams is seen as a key signing to add depth to Hasenhuttl’s defensive options due to the player’s ability to slot in at either left or right-back.
Saints were previously linked to signing Williams on loan during the summer transfer window and it’s thought that the arrival of Telles has made the youngster available for Southampton.