The England worldwide is one of 11 Manchester United players whose current deals are set to expire in June 2019, but he is also one of several the club have been keen to retain.
Calls for Mourinho's departure this season have been slightly subdued following the club's recent comeback against Newcastle United, and officials at Old Trafford continue to insist that their manager's job is still secure.
United have subsequently lost three of their first eight league games - conceding 14 goals in the process - to drop to eighth in the Premier League.
There is interest from German and Turkish clubs and any decision to sign a mid-season deal could further disrupt a hard campaign for the club.
Elizabeth Warren Releases DNA Test Results
However, the report adds, "The analysis also identified 5 genetic segments as Native American in origin at high confidence". That means she could be as much as 1/32nd Native American, or as little as 1/512th. " Elizabeth Warren is a total fraud".
La Viola are keen to keep Milinkovic until at least end of the season and believe they could receive more lucrative offers for him in the summer.
Manchester United manager Jose Mourinho was present in person to watch Milenkovic put in a fine performance in Serbia's 2-0 win over Montenegro on Thursday.
Mourinho will head to his former stomping ground once the worldwide break is over, with a trip to Stamford Bridge to face Chelsea when the Premier League campaign resumes.
They then welcome Juventus to Old Trafford in the Champions League, with Cristiano Ronaldo set to return to his former club.