Italian media outlet Corriere dello Sport, as quoted by Metro, is reporting that the Serie A giants are hoping to secure a huge transfer fee for the 23-year-old.
The same article states that Manchester United view Milinkovic-Savic as a long-term replacement for Michael Carrick, who is set to retire at the end of the Premier League season.
The England international is set to join Mourinho’s coaching staff ahead of the 2018-19 Premier League campaign following a 12-season stint at Manchester United.
According to the same story, Serie A giants Lazio have already turned down a £70m offer for the Serbia international.
Milinkovic-Savic has scored nine goals and has made two assists in 26 appearances in the Premier League in the current campaign.
Manchester United are in second place in the Premier League table but 16 points adrift of runaway leaders Manchester City.
The Red Devils will be looking to close the gap on title rivals Manchester City in the summer ahead of next season.
The 20-time English champions signed Alexis Sanchez in a swap deal from Arsenal in January.
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