The newspaper claim that Matic, 28, is on the verge of quitting Chelsea for United after the terms of the deal were agreed between the two Premier League big hitters.
The Guardian report that United will pay around £40million for the midfield enforcer, who has agreed the terms of a £155,000-a-week deal with the club.
It is said that the Serbia international is set to imminently secure a reunion with former boss Jose Mourinho and that the transfer is likely to be wrapped up this week and will be confirmed at the very latest by the time that United head off to the United States for a pre-season tour starting on 9 July.
Mourinho has made his move for Matic as he attempts to secure a midfield enforcer who can protect the defence and start off attacks in a way that has been the hallmark of veteran Michael Carrick for the past decade.
The 31-times Serbia international was integral to Chelsea’s title triumphs in 2017 and 2015, the latter of which was under Mourinho, who took him back to Stamford Bridge in January 2014 for a fee of around £22million.
Mourinho wants to sign at least four frontline players this summer, with one transfer already in place after Sweden international Victor Lindelof joined from Benfica for £30million.