The 31-year-old struggled for action in the early stages of the 2019-20 campaign and was widely expected to leave Old Trafford either in January or at the end of the season.
United recently activated a 12-month extension on Matic's deal, taking him until the summer of 2021.
However, according to The Sun, the Red Devils now want to open talks over a new two-year contract worth £140,000 a week.
The Serbia international has started nine of United's last 10 Premier League matches and only missed out against Wolverhampton Wanderers at the start of February through suspension. body check tags ::