Hammers boss David Moyes has made securing a new centre-back a priority in the ongoing transfer window and the club were chasing Kurt Zouma.
The Chelsea man has snubbed a switch to the London Stadium though and West Ham are now working hard to push a deal for Milenkovic over the line.
The highly rated Serie A defender has entered the final year of his contract with Fiorentina and the Italian club are prepared to sell him.
West Ham are now close to reaching an agreement with Fiorentina, according to Italian outlet Tutto Mercato, with intermediaries engaged in talks.
It is claimed that West Ham are prepared to pay Fiorentina a fee of €20m to take the defender to the English capital.
Milenkovic has been linked with a host of Premier League sides over the course of the last 12 months.
The centre-back though could be playing his football under Moyes at West Ham when the new Premier League season kicks off.