Jose Mourinho is hoping to complete a deal to sign the midfielder from their Premier League rivals.
The Portuguese is preparing for his first season in charge of the Red Devils, and has drawn up a list of potential additions to go after. And the Sunday People suggest that Matic is one of his main targets after the holding midfielder became a hugely influential member of his Blues squad that won the Premier League title in 2015.
But with it seeming unlikely that incoming Chelsea boss Antonio Conte will be willing to allow one of his key men to leave Stamford Bridge to join one of their main rivals in the Premier League, it appears that Mourinho is prepared to allow Darmian to move in the opposite direction to sweeten the deal.
The 26-year-old has spent most of his first season at Old Trafford as a first-team regular. However, he is a player that Conte knows very well, having worked with him extensively during his time as coach of the Italian national team, and the Sunday People suggests that the former Juventus boss wants to link up with him at Chelsea next season.
Though Matic struggled to find his best form during this most recent campaign, he has shown since he returned to the Premier League in 2014 that he has the ability to be one of the best defensive midfielders in the top flight.
The Serbian's reading of the game can make him incredibly important to the defence he sits in front of, while he also has a creative side that can prove useful going forward, so it is hardly surprising that Mourinho is desperate to get a deal done.