But according to Manchester Evening News, there is a growing acceptance a deal will be too hard to reach with Daniel Levy.
With Michael Carrick now 35 and out-of-contract this summer a new holding midfielder needs to be a prioirty and United have been strongly linked with a move for Eric Dier in recent weeks.
However, the belief at Old Trafford is that the Red Devils are unlikely to succeed in their approach for the England global.
The Manchester United boss is determined to sign a defensive midfielder to succeed veteran Micheal Carrick and bring out the best in Paul Pogba.
Dier, in particular, is interesting Manchester United as they look to strengthen their squad after what has been another disappointing showing in the Premier League in 2016/17.
Matic has been a crucial part of Chelsea's triumphant league campaign and failed to appear in only two of them so far - one of them being their match against Watford, where Conte fielded a rather second-string lineup.
Mourinho was the man who lured Matic back to Stamford Bridge during his time at Chelsea and the 28-year-old played a key role in helping the Blues win the title back in 2015. N'Golo Kante is unlikely to be disposed, which means that any new arrival is likely to take Matic's place in the lineup.
The former Inter Milan and Real Madrid manager is also keen on signing Matic's teammate Willian from Chelsea.
However, Antonio Conte is already looking to add to his thin midfield in the summer, which could put the Serbian's position in the starting eleven in danger.
Mourinho is desperate to add another holding midfielder to his team who can compliment and get the best out of Paul Pogba, and he sees Matic as the ideal heir to Michael Carrick.