Hammers boss David Moyes is focused on signing another centre-back ahead of the new season and is keen on Chelsea’s Kurt Zouma.
However, Chelsea want £25m to let Zouma move and West Ham are reluctant to meet the Blues’ asking price for the Frenchman.
Despite Zouma being open to the move to the London Stadium, West Ham are determined not to be left without a new centre-back and are claimed to have bid for Milenkovic.
It is suggested that West Ham have slapped in a proposal of £14m with Fiorentina for the defender.
Milenkovic has entered the final year of his contract at Fiorentina and the club are expected to sell him if he does not extend his deal.
It remains to be seen if the defender wants to make the move to West Ham.
Moyes’ men have Europa League football to offer in the forthcoming season though and Milenkovic may also want to play in the Premier League.