The Serbian midfielder has been regularly linked with a move away from Lazio for several windows, but the Italian club have managed to keep hold of him.
However, he will be entering the final year of his contract at Lazio this summer and this has led to suggestions that he could finally leave in the coming months.
Lazio are aware of the situation and are prepared to sell only if his suitors agree to meet their asking price.
According to Italian daily Corriere dello Sport, the Serie A giants want €40m before agreeing to sell him.
Clubs such as Arsenal and Newcastle United are keeping tabs on Milinkovic-Savic and are considering making a move for him.
Given his contractual situation, his suitors are plotting to table bids between €20m to €30m this summer.
But Lazio are adamant that their asking price must be met or they will not let him go in the next transfer window.
The Serie A giants are prepared to risk losing him on a free transfer at the end of next season.
While Arsenal may be sure of Champions League football, Newcastle are not and have not drawn up their summer shortlist yet.