The 20-year-old defender is three weeks away from first-team football again after undergoing knee surgery in September
The defender is yet to play this season having undergone surgery in September on a cartilage tear in his knee.
Jones, 20, is on course to return in line with the eight-week lay-off anticipated by United when he went under the knife and has been running at the club’s Carrington training ground for the last two weeks as he strengthens his knee.
"Phil has been working hard, he's slightly ahead of schedule and is looking at the Chelsea game at the end of the month for his return," a United source told Goal.com.
United kept just its third clean sheet of the season in the 3-0 win over Newcastle on Sunday amid a number of injury problems.
However, with Chris Smalling closing in on a return and Jones also making good progress, Sir Alex Ferguson is set to receive a huge boost in the next few weeks.
Jones, who can play at center back, right back or central midfield, made 41 appearances for United last season and has been a success at Old Trafford since arriving from Blackburn for 20 million euros in June 2011.