The 24-year-old picked up a ligament injury during training a fortnight ago.
Jones has since had a brace fitted as a precautionary measure following the incident.
Reports had suggested that the latest setback would see him sidelined for longer than the initial four weeks.
But according to the Daily Mail, Jones could be closing in on a return.
The report suggests he is expected to link up with the United squad again after the weekend.
Jones hasn’t featured for United since January, although it was thought he would play against Feyenoord two weeks ago.
The news will come as a surprise to Jose Mourinho, who probably imagined Jones would miss a big chunk of games.
Mourinho has preferred to partner summer signing Eric Bailly with Daley Blind this season in the heart of defence.
United will be looking to get their Europa League campaign back on track when they face Zorya Luhansk tomorrow (8:05pm).
Related articles
- Man Utd legend: I was bitter about being dropped…but Rooney will fight
- Former Man United star: Wayne Rooney is indispensable to Jose Mourinho
- Jesse Lingard hilariously mocks his Man United teammates