Now in his ninth campaign at Stadio Olimpico, Milinkovic-Savic has already established himself as a legend of the Italian giants.
As many as 64 goals and 59 assists have been contributed in 324 appearances, the Serbia international having previously turned out interest from elsewhere to extend his stay in Rome.
However, with just over 16 months remaining on his contract, the 28-year-old finds himself at a key point of his career as he evaluates his next move.
Lazio, who currently occupy fifth in Serie A with a game in hand, naturally want to agree fresh terms with one of their key men, a deal which would take him past the decade-mark at the club.
Nevertheless, Milinkovic-Savic and his representatives are aware that they will have their pick of teams if they choose not to sign a fresh deal by the summer.
According to Calciomercato, a number of Premier League clubs have already indicated that they are willing to pay €40m (£35.3m) to push through a transfer.
The report claims that Arsenal, Newcastle and West Ham United would all be willing to shell out that fee in order to win the hotly-contested race for his signature.
The Gunners were keen to make such a signing in January but the Premier League leaders eventually opted against bringing in a fresh face for central midfield.
Newcastle have recently been left short in that position due to the departure of Jonjo Shelvey and injury to Bruno Guimaraes, with that area of the pitch expected to be addressed in the summer.
Much may depend on whether Newcastle qualify for Europe, and the same can be said for West Ham who are currently bidding to move away from the Premier League relegation zone.
The Hammers remain in the Europa Conference League, however, and can earn a spot in next season's Europa League if they win that competition.
Despite the level of interest, the report adds that Milinkovic-Savic is solely focused on trying to win silverware at Lazio this campaign with Maurizio Sarri's team also competing in the Europa Conference League.