Markovic, just 17, currently plays for Partizan Belgrade but is already a regular and has scored seven times in 19 appearances this season.
“I really hope I can go to Chelsea, it’s my dream,” Markovic told the English press.
“Chelsea is the place I want to play. I had all the pictures of the team on my wall at home back to when they had Gianfranco Zola.
“And any time they are on TV I try to watch them. For me Chelsea are the best.”
Markovic has a contract with Belgrade until 2016 so Chelsea will have to pay a premium price if they want to land the teenager.