The Sun says the Gunners are eyeing the youngster this month, though face competition from Barcelona and Bayern Munich.
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Kostov has been likened to Barca star Pedri and at 17 is already a senior Serbia international.
With Red Star, the midfielder boasts six goals and five assists in 23 matches.
Telegraf reports Red Star are determined to keep hold of Kostov this month, though are willing to listen to offers over the summer for around €17-20m.
