The 27-year-old's future has been the subject of much speculation in recent months, with a number of clubs believed to be interested in signing him during the current market.
Manchester United, Real Madrid and Paris Saint-Germain have all been linked with his services, while Newcastle United are also believed to be keen on his signature.
However, according to Corriere dello Sport, there is also genuine interest from Chelsea, with Thomas Tuchel's side considering making an offer during this summer's transfer window.
The report claims that Lazio are keen on Blues duo Emerson Palmieri and Ruben Loftus-Cheek, meanwhile, which could place the English side in a strong position to negotiate a possible swap.
The Serbia international was again in strong form for Lazio during the 2021-22 campaign, scoring 11 goals and registering 12 assists in 47 appearances in all competitions.
Milinkovic-Savic only has little over two years left to run on his contract in Rome, though, and he is believed to be open to moving clubs in the current market.
Juventus have recently been credited with an interest, but Lazio head coach Maurizio Sarri has insisted that the midfielder "will not remain in Italy" if he departs this summer.
"Speaking to the president, I have become convinced that if Milinkovic does leave, and that will not happen easily, he will not remain in Italy," Sarri told Goal.
Lazio president Claudio Lotito recently said that the midfielder was not for sale but admitted that "an important proposal from a world-class top club" would be considered.
"Milinkovic is not for sale. I turned down €140m (£120m) bid for him [years ago]", Lotito told Rai Sport. "I'd ask Sergej what he wants to do only in case we receive an important proposal from a world-class top club."
The midfielder has scored 58 goals and contributed 51 assists in 294 appearances for the Italian club since arriving from Genk in August 2015.
There has recently been speculation surrounding the futures of N'Golo Kante and Jorginho at Stamford Bridge, and Tuchel is allegedly keen to boost his midfield options for the 2022-23 campaign.
Chelsea have also recently been credited with an interest in Robert Lewandowski, but the Bayern Munich forward is reportedly intent on joining Barcelona during this summer's transfer window.