According to ESPN FC, the Red Devils are set to secure the deal for the Serbian international before the end of the week. The 28-year-old played under Jose Mourinho when the latter was in charge at Stamford Bridge.
The Portuguese tactician re-signed the midfielder for the Blues from Benfica in January 2014. He played a key role in their title winning season under Mourinho at Chelsea. The United manager now wants to reunite with his former player at Old Trafford, who would cost them £40m ($50.9m).
Matic has emerged as a priority signing for the former Inter Milan and Real Madrid manager. Mourinho has identified the need to strengthen the defensive midfield position and Tottenham Hotspur's Eric Dier had earlier emerged as the main target.
United have received no encouragement in their efforts in signing Tottenham's England international star. The situation has forced them to look elsewhere and have identified him as the main target. It was earlier reported that Matic had verbally agreed personal terms with the Red Devils. However, that has been rubbished by the club.
Chelsea manager Antonio Conte has identified AS Monaco's Tiemoue Bakayoko as the player to strengthen his side's midfielder. The 22-year-old France international is expected to complete his £35m ($44.6m) move to the west London club.
The Blues are confident of securing the deal for Bakayoko before they fly to China for the pre-season. His imminent arrival will allow them to sanction Matic's sale, who will complete his move to United.
Mourinho will take his men to the United States for the pre-season tour. United will fly on 9 July and the Red Devils boss wants a majority of his signings to travel with the squad early next month. Victor Lindelof, who arrived from Benfica, is the 20-time English champions' only signing so far this summer.
Real striker Alvaro Morata and Inter Milan's Ivan Perisic have also been identified as transfer targets. However, no deal is closer towards completing as Matic is expected to be United's second summer signing.