SunSport reported that the United boss watched the Serbia midfielder, 23, in Thursday’s 2-0 UEFA Nations League win over Montenegro and remains interested.
Mourinho made it clear he wanted the Lazio star before the World Cup but his asking price rose after the season ended.
United walked away from the deal but Mourinho is eyeing a January deal if a fee can be agreed.
Milinkovic-Savic agreed a new deal with Lazio this month, which will ensure they get top dollar for the ex-Genk midfield man.
His fee could beat the £89m for Paul Pogba, whose future has been thrown in doubt this term.
SMS is seen as an ideal partner for countryman Nemanja Matic in United’s engine room.
Mourinho will be able to use his Chelsea pal Mateja Kezman to help land Milinkovic-Savic.
Former Chelsea forward Kezman — one of Mourinho’s first signings in England — is agent to the midfielder.
And that relationship with the Special One puts the Red Devils in pole position to land his player despite Europe’s top clubs looking to swoop.
Mourinho also wanted to add Inter Milan midfield ace Ivan Perisic to his attack but could not agree a fee for the Croatian.
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