The 29-year-old played the full 90 minutes against Wolverhampton Wanderers in the Premier League on January 3 - his first appearance for the club in nearly two years.
Jones is believed to be available for transfer this month, with a number of clubs said to be showing an interest, but according to the Daily Star, Man United want £15m for the Englishman.
The report claims that Burnley are keen on the defender but would not be prepared to match his club's valuation or pay his £100,000-a-week wages.
Jones impressed on his return for Man United against Wolves but was back on the bench against Aston Villa on Saturday, and Eric Bailly, Raphael Varane, Harry Maguire and Victor Lindelof are all ahead of him in the pecking order.
The former Blackburn Rovers youngster has made 225 appearances for the Red Devils since arriving in 2011, winning one Premier League title and one FA Cup. body check tags ::