The Daily Mail says Chelsea are close to finalising an initial, £8million deal for Markovic, 18.
The midfielder has already been capped by his country and scored in a friendly against Chile last month.
He has also scored six goals in 12 games for his club, Partizan Belgrade, this season.
Liverpool, Arsenal and Inter Milan have all been negotiating with Partizan, who want a deal which eventually rises to around £14m based on appearances. However, Chelsea are the player's preferred option.