According to The Sun's Mike McGrath, Mourinho still wants to recruit the midfielder despite the fact that United pulled out of the race to sign him in the summer when his £80 million valuation went up.
The manager is hoping a deal could be done in January, though the fee could exceed the £89 million spent on Paul Pogba after Milinkovic-Savic signed a new contract with Lazio earlier in October.
McGrath said Mourinho can use his relationship with Kezman—who was one of his first signings during his first spell at Chelsea—to help expedite the process, putting United in "pole position" ahead of other interested parties, which include some of Europe's elite.
Milinkovic-Savic was flattered to hear Mourinho attended Serbia's UEFA Nations League match with Montenegro on Thursday to watch him, per football journalist Milos Markovic:
Mourinho's continued interest in him is of no surprise to football writer Ryan Baldi, who believes the 23-year-old to be a perfect fit for the manager:
The Lazio star is most effective in the final third, as evidenced by his return of 14 goals and nine assists in all competitions last season.
That's not to say he can't help out defensively, though—he's an all-rounder in midfield with a 6'4" frame that allows him to be physically robust, and he also boasts an impressive level of technical skill.
However, regardless of Mourinho's relationship with Kezman, he would be an expensive addition to United's midfield, and they have already splashed out on Pogba as well as spending £40 million on Nemanja Matic and £47 million on Fred.
United did not sign a new centre-back in the summer after backing Mourinho with a combined £60 million for Eric Bailly and Victor Lindelof, so they may be similarly reluctant to make another costly purchase in an area in which they have already invested heavily.