The story comes from Tuttosport in Italy, suggesting that Milinkovic-Savic fits the profile outlined by Real president Florentino Perez of 'the best players in the world' and that the Serbian would fill a growing 'hole' in midfield.
Equally, Tuttosport clams that Madrid have eyes for Juve's Miralem Pjanic in a similar capacity.
The important factor to note there is that the Italian champions would apparently not sell Pjanic for anything less than €100m, which, if several recent reports about Real's transfer policy are to be believed, actually make it a rather prohibitive price tag.
Assuming that Real were to make a move for Pjanic and meet the €100m valuation, it is said Juve would then take that money and spend it on Milinkovic-Savic themselves.
But given that Real have been more interested in signing younger talents in recent years, logic dictates that Los Blancos would be more interested in the Serbian than the Bosnian, with Milinkovic-Savic still only 23 years of age and Pjanic due to turn 29 on his next birthday in April.
Milinkovic-Savic has been labelled a €155m player this summer, but without Premier League clubs to bloat the transfer market because the English deadline has now passed, Lazio could be forced to lower their demands if they have a genuine willingness to sell their biggest asset.