The 18-year-old has attracted attention from a number of Europe's top clubs, including Barcelona, Roma, and Sevilla. But Inter Milan reportedly lead the pursuit, with Arsenal close behind, although the Gunners risk losing out to the Italian side.
The report claims Arsene Wenger has been tracking the FK Partizan Belgrade midfielder for the past few months, and could be tempted to make a move when the transfer window reopens in January.
But Inter are expected to register their interest in the coming weeks, and could even submit an offer for the talented youngster.
The Italian giants got a first-hand look at Markovic when Belgrade visited the San Siro for a Europa League match in October, and Inter boss Andrea Stramaccioni was impressed by what he saw, according to the report.
Inter travel to Belgrade for the return fixture this week, and Italian sources claim the Serie 'A' league leaders will take the opportunity to assess Markovic further.
Arsenal squandered a 2-0 lead against Schalke in the Champions League last night, but the Gunners still look favourites to progress from Group B.
Arsene Wenger's side took an early lead through Theo Walcott, before Olivier Giroud doubled their advantage. But goals from Klaas-Jan Huntelaar and Jefferson Farfan pegged the Gunners back and they had to settle for a share of the spoils.