Newly promoted Fulham want to sign midfielder this summer, according to reports.
Matic, 33, is out of contract at Old Trafford at the end of the season and is set to leave on a free transfer.
Fulham are looking to add Premier League experience to their squad ahead of their return to the top flight.
According to , Matic fits the bill for the Cottagers, who will try to persuade him to stay in England.
It is believed the Serbian has offers from abroad, with Juventus also keen on his signature.
Matic rose to prominence in English football with Chelsea when he won the league title in west London in 2015 and 2017.
Since moving to the Red Devils, he has struggled to reproduce the form he showed at Stamford Bridge and has not won a trophy with the club.
However, in recent games, he has started for United alongside Scott McTominay in central-midfield showing he is still capable of playing at a good level.
Between Chelsea and United, the midfielder has made nearly 250 appearances in the Premier League.
It was thought a fresh start under new manager Erik ten Hag could convince him to stay with the Manchester giants.
But last month Matic revealed he would be leaving the club following a statement made via social media.
He said: ‘After a great deal of thought, I have decided that this season will be my last with .
‘I have informed the board, the manager and the players of my decision.
‘It has been a huge honour and a privilege to play for this great club. A big thank you to the fans for their unwavering support.
‘I will now give everything until the end of the season to help my teammates finish as strongly as possible.’
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