The 23-year-old Serbia international is one of Serie A's hottest properties and has been linked with several of Europe's biggest clubs in recent months.
Scouts from Liverpool, Man City and Tottenham were all in attendance at the Stadio Olimpico earlier in the month for Lazio's 4-1 win over Genoa, with Sergej Milinkovic-Savic the reason for their visits, according to a report.
The 23-year-old Serbia international is one of Serie A's hottest properties and has been linked with several of Europe's biggest clubs in recent months, including Manchester United, Juventus and Real Madrid.
However, while he stayed put in the summer amid talk of a new contract at Lazio, the interest in his services only appears to have ramped up with the Premier League trio of Liverpool, City and Spurs apparently sending scouts to monitor his performance against Genoa on September 23, according to the Mirror.
The powerful midfielder scored and registered an assist on that outing, while he netted 12 in total in Serie A last season.
Despite the continued interested, Lazio are apparently confident they can tie Milinkovic-Savic down to a new contract (his current deal expires in 2022), with owner Claudio Lotito revealing he rejected an 'obscene' offer from an unnamed club at the end of the summer window.
“I made a pact with the coach that I wouldn’t sell him over the summer,” he told Il Tempo (via Football Italia). “We received a very big offer for him a day before the market shut and we had a plan to replace him, but there wasn’t enough time.
“When a bid arrives on August 17 and the market shuts a day later, I couldn’t sell him, above all for the promise I made to the coach. I honor the promises I make."
Lotito revelation that the bid came on August 17 effectively rules out the possibility that it came from an English club, with this summer's deadline for Premier League teams passing on August 9.
He added: “I won’t mention figures, but certainly it was an obscene offer that I think no one else in Italy could’ve refused. We’ll see if I was right or wrong to do what I did. I could’ve sold him for a lot of money but didn’t.”