The Serbian midfielder has attracted admirers from across Europe after several impressive seasons with the Roman club.
And the Mail Online reports that the Blues are casting an eye over his progress, despite currently being in the middle of a two-window transfer ban.
Frank Lampard is said to consider the 24-year-old as his successor in the Chelsea midfield as the Premier League side weigh up a sizeable bid for next summer, when their embargo will be lifted.
The club were slapped with the punishment by Fifa after breaking rules over the signing of youth players.
Lazio rate Milinkovic-Savic very highly and have held out for a sum of more than €100 million in the past.
However, those demands may have dropped by the end of the season to a more reasonable €60m, according to the outlet.
A physical powerhouse with a superb touch and eye for goal, Milinkovic-Savic has been one of the standout players in Serie A over recent seasons and won the league’s Midfielder of the Year award for 2018/19.
This season, he has two goals and four assists to his name in 11 appearances across all competitions.
Thursday wasn't a night to remember for the Serbian though, as Lazio threw away a 1-0 half time lead to lose 2-1 at Celtic Park thanks to a late Christopher Julien header.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.