Manchester United have been backed to move for the Chelsea star, who Mourinho managed during his time at Stamford Bridge.
The Portuguese is reportedly keen to sign a midfielder this summer, despite already having the likes of Paul Pogba, Marouane Fellaini, Ander Herrera and Michael Carrick at his disposal.
Matic starred under Mourinho when Chelsea won the Premier League in 2015, and was again key in the Blues' title triumph under Antonio Conte this season.
As a result, United are considering a move to bring him to Old Trafford.
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Chelsea star Nemanja Matic could join Manchester United this summer
Manchester United are reportedly closing in on the signing of Chelsea star Nemanja Matic
And the Manchester Evening News are claiming that Matic has discussed the prospect of reuniting with Mourinho – with a deal dependent on whether the two clubs can agree a fee.
It is said Mourinho wanted to sign the 28-year-old a year ago, but Conte refused to sanction a move given how pivotal he was to his plans.
The midfielder started 30 of their 38 league games, pocketing a second winners medal in three seasons in the process.
Matic's current contract expires in 2019 and Chelsea could let him leave if he does not want to extend his deal.
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Nemanja Matic could be set to reunite with Jose Mourinho at Manchester United
The report adds that the deal is close to being agreed, with Matic on a list of four players Mourinho told chief executive Ed Woodward he wanted snapped up.
Express Sport understands Atletico Madrid hitman Antoine Griezmann is another player he wants, while Inter Milan goalkeeper Samir Handanovic could move to Old Trafford if David De Gea jumps ship to Real Madrid.
The last player to move from Chelsea to United was Juan Mata, who has won three major trophies since arriving in January 2014.