The Stamford Bridge manager has been impressed by Markovic, who scored his first goal for Serbia in a friendly against Chile last month. But the youngster is attracting interest from a number of clubs, including Liverpool.
The teenage midfielder is rated as one of the most talented players of his generation, and a bid in the region of £8m will likely be required to bring Partizan Belgrade to the negotiating table.
Markovic has established himself in the Partizan first-team this season, and already has six goals in 12 games for his club.
The report claims Liverpool, Arsenal and Inter Milan have all held talks with Partizan over Markovic, but the Serbian club are believed to be holding out for a fee closer to £14m with appearance fee add-ons.
But Markovic is thought to prefer a move to Chelsea. So Liverpool and Arsenal could be left to explore other targets, while Chelsea are expected to be extremely active in the New Year.
The report also suggests the Stamford Bridge hierarchy have drawn up a list of possible alternatives, including Bayer Leverkusen forward Andre Schurrle, Altetico Madrid striker Radamel Falcao, Real Madrid frontman Gonzalo Higuain, or Newcastle's Demba Ba.
The Blues seem to be set to move for a striker next month, as Rafa Benitez can only call on Fernando Torres and Danny Sturridge at the moment.
Liverpool have striker concerns of their own, and were forced to play Jonjo Shelvey in a 'false nine' role against West Ham on Sunday.