According to the Daily Mail, the Serbian international will swap the west London club for the Red Devils in the coming days. The midfielder will turn 29 on 1 August, and has already informed the Blues that he is looking for a move away from the club in the summer transfer window.
Chelsea have already completed the signing of Tiemoue Bakayoko from AS Monaco. It was earlier believed that the arrival of the France international will see the Premier League winners sanction Matic's sale to United.
However, the Stamford Bridge outfit's manager Antonio Conte will ideally allow the former Benfica man reunite with Jose Mourinho at Old Trafford if Chelsea secure the signing of another midfielder.
The English champions' owner Roman Abramovich was also open to the idea of allowing the midfielder join the 20-time English champions for his five-and-a-half year spell at Chelsea over two spells.
Mourinho re-signed Matic for the Blues in January 2014, when the former was in charge at the Bridge. Since then, he has played a key role in helping his current employers win two league titles.
Matic's desire to leave Chelsea this summer has seen him drop from Conte's squad for the pre-season trip to China and Singapore. He has interest from England and Italy as Juventus are also looking at the option of signing him.
Chelsea value their midfielder around £40m ($52.3m). The Turin club are unwilling to meet Matic's asking price and also decided against handing the length of the contract the Serbian sought.
This has come as a welcome boost for United, who have long maintained their interest in the Premier League star. Mourinho was keen on bringing him to Old Trafford in his first summer transfer window at the club.
Matic decided against leaving Chelsea last summer and went on to win the league. The 28-year-old, along with Diego Costa has been left out of the pre-season squad, and Conte has stressed that he needs complete control at the club.
Mourinho has already stressed that he needs to bring in two more players to club in the transfer window. He has set his sights on sign a midfielder and an attacking player.
With Matic closing in on Chelsea exit, it will come as a welcome boost for Mourinho and United. Should they manage to land him, the Blues midfielder will be the Red Devils' third summer signing after Victor Lindelof and Romelu Lukaku.