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.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.