The 22-year-old netted seven times in 38 appearances for the Biancocelesti last term and has been trusted with the captain's armband early on this season.
Milinkovic-Savic's impressive form has not gone unnoticed, as his agent has suggested that the Manchester clubs are battling it out for his signature, while also hinting that Atletico Madrid, Real Madrid, AC Milan and Inter Milan may join the race.
"There's been a lot of interest from several clubs, such as those in Madrid, Manchester and Milan," Mateja Kezman, formerly of Chelsea, told Radio CRC. "But he wants to be happy, to play to keep growing and become one of the best in his role.
"It's difficult to see him away from Lazio, where he has started the season very well, but I can't rule out him leaving. If Milinkovic-Savic keeps this up, there will be plenty of contact from different clubs, like there was [in the summer].
"We'll see what happens but, for now, what matters is that he's growing under [Simone] Inzaghi, who's a great coach. Right now, Milinkovic-Savic is happy to continue his adventure in Rome with Lazio."
Lazio are said to value the central midfielder in the region of £26m, two years after he arrived from Belgian club Gent.