If Lazio do cash in to Manchester United then they will have a huge windfall to spend, but having Grujic on board already gives them freedom to strengthen elsewhere, with a replacement also needed in defence of Stefan de Vrij, who has signed for Inter.
The Lazio midfielder has been linked with a move away from the Biancocelesti, particularly since they slipped out of the Champions League places on the final day of the Serie A season.
Milinkovic-Savic hit the headlines this season after a stunning year in which he netted 14 goals and supplied eight assists.
The report states that Milinkovic-Savic has been linked with serious interest from Man United for a prolonged period but Real could now be the front runners in the race to sign the 23-year-old Serbian midfielder.
Manchester United want to sign Milinkovic-Savic and are aware of Lazio's £100m valuation.
But, Jose Mourinho has himself iterated that he will be on the lookout for two midfielders this summer if Marouane Fellaini leaves, which looks like a distinct possibility, means the Red Devils are still in the market for one more midfield addition.
It is not only the interest from Juve and Real that perhaps makes the eventuality of Milinkovic-Savic joining United now unlikely.
Lazio may sell Sergej Milinkovic Savic for the right price.
Florentino Perez is set to make some big changes to the Real Madrid squad this summer, with the squad set to be overhauled.
In fact, according to reports in Il Messaggero Los Blancos are willing to offer a further £18 million in performance-related bonuses.
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