The Daily Mail says there were fears that Jones may be out for five to six weeks after catching a stray elbow in the face from Clint Dempsey as United won 5-0 at Fulham in the Barclays Premier League.
However, it is understood that United were more optimistic that the 19-year-old had suffered severe bruising. If that is the case, he may even be available for the Boxing Day fixture at home to Wigan.
Jones was examined at United's training ground and was then sent to hospital for an X-ray in the afternoon. Those results are not yet known and will be revealed by manager Sir Alex Ferguson at his weekly press conference.