The 25-year-old has developed into a key player for Benfica since joining the club from Chelsea in 2009.
Matic was strongly linked with a return to Stamford Bridge last summer, but a return to the Blues now seems unlikely.
Benfica would be ready to cash in on the Serbian midfielder as they are struggling to make the next stage of the Champions League.
The Sun reports that United are now ready to go head-to-head with rivals Liverpool in the race to sign the midfielder.
What is your opinion? Feel free to discuss the article under. You have to comment by using your Facebook profile. Be fair and have respect for other people and opinions!
Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.