United have been made aware of the Serbia international's availability on several occasions for a lower fee of £70million, but increased interest in the midfielder has ramped up his market value.
Mourinho's side have reportedly scaled back their interest due to the inflated figure that Lazio are demanding and having struggled to see where the 23-year-old could fit in with their squad.
Old Trafford is set to welcome Shakhtar Donatsk's Fred as negotiations conclude in a £50million move. The midfielder will slot in comfortably alongside Nemanja Matic and Paul Pogba, so it is difficult to see where Milinkovic-Savic could go.
At this point, United are continuing talks with Marouane Fellaini as they hope to extend his contract, despite having already received an offer from AC Milan, but may well be in search of another midfielder come the summer.