The Rossoneri have been linked with a move for the Serbian, but his price tag means a move to San Siro can't happen, at least this summer.
The Red Devils have only signed Lee Grant, Diogo Dalot and Fred so far this summer ahead of Jose Mourinho's third season in charge of the club.
The 23-year-old is reportedly being tracked by Lazio's Serie A rivals Juventus and AC Milan as well as Real Madrid and Manchester United, but Lotito said no offers for the player have been made since 2017.
Jose Mourinho has spent most of pre-season in a haze of anger due to the clubs lack of transfer activity but there is still time for the wallet to be opened. The Serbian midfielder has developed into one of the most exciting midfielders in the game, since moving to Lazio back in 2015 from Belgian side Genk.
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Milinkovic-Savic has also been on Man United's radar and fits the profile of a Paul Pogba replacement. In order to do so, the Red Devils will have to smash their transfer record, with Lazio demanding €155 million for their prized asset.
According to the same story, Manchester United, Juventus and Real Madrid are all keen on signing the midfielder this summer.
Barcelona have already had a bid rejected by Manchester United for Pogba this week and the final few days of the transfer window are set to be extremely interesting for observers of the Old Trafford outfit.
Interestingly, the reigning European champions also remain keen in acquiring the services of the seven-time capped Serbian worldwide.