Club sources confirm Milenkovic remains an option for the centre back position left vacant by the departure of Fabian Balbuena but there are a number of other options in the same position should they not be able to get this deal over the line.
The Hammers are not the only club involved in a move for the Serbian defender the deal is not as close as some are reporting.
Juventus are also said to be interested in the central defender but have yet to make a bid and that could delay the player agreeing on personal terms with West Ham. The reported transfer fee between the two parties is said to be €20m (£17m).
Fiorentina appears to be already lining up a replacement in Matija Nastasic.