The 23-year-old, who was voted the Red Devils' Player of the Month for August, looked set to miss at least two matches due to Football Association guidelines regarding head injuries.
United have suggested that Shaw could return earlier if they meet various criteria, though, meaning that he could yet been named in the squad to face Watford at Vicarage Road.
"Jose Mourinho could be without Luke Shaw, who sustained a head injury in England's UEFA Nations League match against Spain at the weekend," an article on United's official website read.
"Some reports suggest the left-back will be obliged to serve a mandatory seven-day concussion period of absence, though this has not been confirmed.
"Shaw has enjoyed a bright start to the season for United, picking up the Goal of the Month and Player of the Month awards for his performances in August, and will be assessed by United's medical staff before any decisions are taken.
"After the trip to Watford, the Reds' next fixture is away to Swiss side Young Boys in the Champions League on Wednesday."
United are expected to be without Marouane Fellaini this weekend, however, as the Belgian midfielder "sustained a minor back problem" during the international break.