They are aware a deal will be in the reign of around £40m as Jose Mourinho sees bringing in a new defensive midfielder as the main priority for this summer.
He is still looking to sign a wide player and a full-back, but the Serbian remains a top target having played with him at Stamford Bridge.
Man United felt Chelsea would refuse a transfer due to both the hijacking of their bid for Romelu Lukaku from Everton, however, Chelsea’s recent progress in the transfer market has given the Old Trafford hierarchy renewed confidence about the deal.
The fact that Matic wants to go to United above anywhere else also helps even with strong interest from Juventus and Internazionale as it could also reduce a potential fee.
Mourinho had also identified Eric Dier for the position but it was clear that Tottenham Hotspur were impossible to deal with, totally unwilling to sell the Englishman.
He has been disappointed with the lack of progress so far but still expects two more players before the end of the window in Matic and Ivan Perisic.