That’s according to Italian journalist Fabrizio Ponciroli, who says it is “plausible” for the Lazio midfielder to head to west London.
Milinkovic-Savic is one of the world’s most in-demand stars with a cluster of top clubs thought to be keeping tabs on him.
Manchester United, Juventus, Real Madrid and Paris Saint-Germain have all been linked with the £134m-rated (€150m) Serbian.
While reports in Italy suggest Chelsea and Manchester City are showing interest in him as the transfer window draws to a close.
Ponciroli, who works for magazine Calcio 2000, has now offered his take on Milinkovic-Savic.
And he’s suggested that where the 23-year-old’s future lies will become clearer if he does not appear at Lazio’s training camp today.
“I know that Chelsea is thinking about him seriously and it is a plausible track,” Ponciroli told RMC Sport last night.
“If tomorrow he does not show up for medical visits, it means that his adventure in Lazio is over.”
Chelsea have already bolstered their midfield this summer with the capture of Jorginho from Napoli.
Maurizio Sarri faces disappointment in the hunt for Milinkovic-Savic if the Lazio ace listens to his father.
Nikola Milinkovic has revealed he wants his son to head for Juventus if he calls time on his Stadio Olimpico career.
“I’ve told him many times that Juventus would be perfect for him, the ideal club,” said Milinkovic.
“In Turin there is a prestigious club with multiple trophies that has been dominating the scene for years. He’d have the opportunity to grow and improve until reaching full maturity.
“After three seasons in Rome, Sergej knows the Italian championship perfectly, he has settled and integrated in a big way, he has learned the language well.
“With top quality teammates like Paulo Dybala, Douglas Costa and so forth, he could win the Scudetto, Coppa Italia and why not give an important contribution to triumph in the Champions League?
“Juve always go far in that competition and if they were to win the most prestigious trophy, Sergej could even dream of the Ballon d’Or.”