Chelsea romped to the Premier League title in their first season under Antonio Conte.
Matic, 31, was a first-team regular, making 35 top flight appearances.
But he is being heavily linked with a move away from west London as Conte looks to reshape his squad this summer.
And a reunion with Jose Mourinho at Old Trafford was seemingly on the cards for the Serbia international.
The United boss parted with £21m to sign him from Benfica during his second spell in charge of the Blues three years ago.
Starsport understand the Red Devils have already agreed a £40m fee with Chelsea and personal terms with Matic.
But The Sun claim Mourinho is now considering pulling out of a deal.
He is said to believe his old club are stringing him along while they chase a replacement for the midfielder.
Chelsea's £35m move for Monaco star Tiemoue Bakayoko is dragging on while they have also been credited with interest in Radja Nainggolan of Roma.
