That is according to bookmaker BetStars, who have priced the Red Devils at 6/4 to complete a swoop for the Chelsea midfielder.
Matic faces an uncertain future at Stamford Bridge despite playing a key role in their Premier League title triumph last term.
Chelsea are closing in on a deal to sign Monaco midfielder Tiemoue Bakayoko, which could leave him vulnerable to the chop.
According to the Manchester Evening News, Matic has agreed personal terms on a move to United.
And that would mean linking up with former Chelsea manager Jose Mourinho at Old Trafford.
Ian Marmion, director of trading at BetStars, said: “Nemanja Matic looks like he could be the first Chelsea player to head for the exit door at Stamford Bridge this summer, with the odds suggesting a move to Manchester could be on the cards.
“Manchester United have emerged as the clear 6/4 favourites to sign the Serbian international, ahead of Juventus at 8/1 and Bayern Munich at 10/1.
“The opportunity to reunite with former manager Jose Mourinho, who signed Matic at Chelsea, could prove too good an opportunity to ignore.
“Expect to see Matic in a United shirt next season.”