The 25-year-old withdrew from the England squad to face Brazil after suffering the recurrence of an old thigh injury during the goalless draw with Germany at Wembley.
Three Lions boss Gareth Southgate had expected Jones to be "fine" for the second friendly but he returned to United for further treatment.
Subsequent scans have however proven positive and Jones is optimistic he could be involved for the visit of Newcastle to Old Trafford on Saturday [18 November], according to The Guardian.
Jones initially picked up the problem in the defeat to Huddersfield Town in mid-October but played the full 90 minutes of the 1-0 success over Tottenham Hotspur and over an hour of the defeat to Chelsea prior to the international fortnight.
He started the stalemate against the world champions on Friday [10 November] with heavy strapping on his left leg but was replaced by Liverpool's Joe Gomez after just 25 minutes.
Of United's current four-man injury list Jose Mourinho expects Zlatan Ibrahimovic, Marcos Rojo and Paul Pogba to all return before the hectic Christmas schedule.
Michael Carrick's return is less certain however with United's medical officials baffled by a mystery illness which has emerged off the back of a calf problem. The 36-year-old, who is out of contract in the summer, has played just once this season.
Reports suggest that of those players honing in on a first team return midfielder Pogba is the closest to resuming his campaign. The France international has not played since the second full week of September due to a hamstring injury, but has resumed training with the senior team during the international break, according to The Daily Telegraph.
Newcastle will arrive at the home of the 20-time English league champions with a three-man injury list. Winger Christian Atsu appears destined to miss out having aggravated a thigh problem while on international duty, while Mikel Merino is nursing a back issue. Full-back Paul Dummett is a long-term absentee having played just once this season due to a hamstring blow.