22-year-old Milenkovic is one of the most talented young defenders in Serie A and many clubs have been watching him.
In their search of a central defender, West Ham have come forward with a formal offer for the Serb.
Fiorentina have not rejected the bid, although they are waiting for a bigger proposal. A move to AC Milan was mooted earlier in the window.
Milenkovic played the full 90 minutes in both of Fiorentina’s opening games of the new season.
Since his arrival from Partizan Belgrade in 2017, the 20-time Serbian international has made 98 appearances for the Viola.
West Ham’s scramble for a new centre-back has seen them miss out on James Tarkowski and Wesley Fofana.