Tuttosport says Chelsea are lining up a move for Milinkovic-Savic for the summer market.
Blues management have concerns about their goalkeeper options, with Robert Sanchez and Filip Jorgensen failing to convince.
In contrast, Milinkovic-Savic's reputation continues to grow after another impressive campaign with the Granata.
Also watching developments are Manchester City, with doubts over the future of Ederson.
Milinkovic-Savic has a deal with Toro to 2026 and a buyout clause of €20m.
Interestingly, Milinkovic-Savic was signed by Manchester United as a teenager, but UK work permit difficulties saw the Serb fail to actually move to Old Trafford.