Stoke City assistant manager Mark Bowen also revealed the club would be interested in signing Jones and was hoping a deal could be reached.
Arsenal are said to be keeping a close eye on the Englishman as Arsene Wenger continues his desperate search to improve his defensive options.
Despite being linked with numerous clubs this summer, the 24-year-old looks set to stay at Old Trafford and wait for his chance under Jose Mourinho.
Jones only made 10 Premier League appearances last season and struggled to keep himself fit or cement his place in the first-team.
Now while he is finally back to full fitness, he has fallen further down the pecking order under Mourinho following the arrival of Eric Bailly.
It is understood Jones is still a part of Mourinho’s plans and the Portuguese boss could be looking keep his options open as he approaches the month of September.