Markovic, who made his Serbian national team debut aged 17, is one of the most exciting young players in Europe.
Chelsea have been watching the 19-year-old old extensively in action for Partizan Belgrade and Serbia, along with a host of other top European clubs.
And Markovic recently revealed he feels he would thrive in the Premier League.
"A lot of people say that maybe I'm not suited to the English league," Markovic said as reported by the Daily Mirror.
"But I can tell you that I love the Premier League and I see it as an ideal stage for me."
The report claims the return of Jose Mourinho to Stamford Bridge could accelerate a deal for Markovic, as the former-Real Madrid boss looks to strengthen early.
He's keen to mould the squad inherited from Rafa Benitez into his own image, while continuing Chelsea's recent tradition of buying the world's top young players.
Last summer, the Stamford Bridge club splashed out for Eden Hazard from Lille and Oscar from Internacional, while Victor Moses and Cesar Azpilicueta also joined.
All were 23 or younger at the time they signed for the club.