The 23-year-old defender will have a year left on his deal with Fiorentina in the summer and is widely expected to leave the club at the end of the season.
A move to the Premier League has been mooted, with Liverpool and Tottenham aware of Milenkovic’s situation and having tested the water with his entourage.
Manchester United and Inter are also potential destinations for the Fiorentina player, whose contract at the Serie A side runs out in the summer of 2022.
Fiorentina have not given up on convincing him to sign an extension, but according to Italian outlet Calciomercato.com, the Italian giants are acutely aware that the chances of the defender signing a new contract are low.
Milenkovic has almost made up his mind about leaving Fiorentina and trying out a different experience from next season onwards.
A move within Italy is also a possibility, but he may receive lucrative offers to move to England.
Fiorentina wanted a fee of €40m last summer for Milenkovic and the price is expected to come down to around €30m in the coming months.