This has been reported by the Telegraph, who claim that Portuguese tactician Mourinho was hopeful of being reunited with Matic ahead of the 2016/17 campaign.
The Serbian international enjoyed a wonderful season for the Blues during their title-winning campaign but struggled to replicate his form last season.
Chelsea want to keep Matic
Mourinho, who is expected to be named as the next Manchester United manager imminently, may well want to bring him to Old Trafford, but it appears that incoming Blues chief Antonio Conte is keen to work with the player.Conte, who will lead Italy to this summer's European Championships, will take over at Chelsea on a permanent basis ahead of the new season.
And, while it appears that he's ready to shake things up in the middle of the park in west London - Radja Nainggolan from Roma has been heavily linked to the club - Matic will still be handed a chance to shine at Stamford Bridge.
It appears, then, that United may have to give up on Matic before their pursuit has even started.
United options
But what does the future hold for Manchester United's midfielders under Mourinho's regime?Well, Bastian Schweinsteiger will surely be desperate to prove his credentials on English soil after a disappointing campaign in Manchester. The former Bayern star was once recognised as one of the leading midfielders in world football, but he looked a shadow of his former self in the last campaign.
Michael Carrick, meanwhile, could leave the club on a free transfer with his contract set to come to an end imminently. The former Tottenham midfielder is still one of United's most consistent midfielders, however, so Mourinho should think twice before allowing him to exit.
Belgian international Marouane Fellaini and Spaniard Ander Herrera have been in and out of the United team over the last couple of seasons and they still have it all to prove at the club.
Morgan Schneiderlin, who arrived from Southampton last summer, just hasn't been able to reach the required standard this season, but surely he will be able to bounce back under Mourinho.
Then there's versatile captain Wayne Rooney, who spent the final stages of this season in midfield. It will certainly be interesting to see what the self-proclaimed 'Special One' does with the United ace.
Manchester United fans: should Mourinho sign a new midfielder for your club? Have your say below!