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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Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.