The Serbian defender has a year left on his contract with Fiorentina and has been heavily linked with a move away from the Italian club in the ongoing transfer window.
West Ham pushed to sign Milenkovic and looked set to get a deal over the line before talks faltered and they turned to other options.
According to Italian broadcaster Sportitalia, Tottenham are now the main contenders to secure Milenkovic’s signature.
However, Fiorentina are putting in serious effort to try to convince the player to pen a fresh deal and they are claimed to be making rapid progress.
The talks are progressing between the two camps and there is confidence that an agreement could be reached soon.
Tottenham continue to be keen on Milenkovic and the Premier League side will be watching developments closely as they consider their options.
Fiorentina want to sell Milenkovic if they cannot convince him to extend his contract at the club.
