The Serbia international was brought back to Stamford Bridge by Mourinho in 2014, having initially been sold to Benfica three years earlier.
Matic won the Premier League title with Mourinho's side in 2015 and repeated the feat with Antonio Conte's Blues this past season, featuring in 35 of their 38 league games.
The Red Devils have reportedly agreed on a fee of £40 million for the 26-year-old, who is expected to undergo a medical on Wednesday.
The midfield enforcer is seen as a long-term replacement for United stalwart Michael Carrick and would become Mourinho's second off-season signing following the recent arrival of defender Victor Lindelof from Benfica.