Spurs are in the market for a new centre-back and have been linked with a clutch of players, including Fiorentina star Milenkovic.
The Serbian has entered the final year of his contract at the Stadio Artemio Franchi, and it has been claimed Spurs slapped in an offer for him, which Fiorentina considered to be too low.
It has been suggested that Tottenham have notified La Viola that they might return for the defender with another offer.
However, according to Italian daily Gazzetta dello Sport, Fiorentina have accelerated proceedings to clarify Milenkovic’s contractual situation at the club and have proposed a new deal.
The Serie A side have offered a two-year contract extension to the 23-year-old, but they are yet to hear back from the player or his representatives
Spurs have made it clear that they will not return to the table for Milenkovic before 20th July, but they could be dealt a blow if Milenkovic decides to stay in Florence.
But if Milenkovic knocks back Fiorentina’s offer, they are tipped to put him up for sale with a minimum fee of €15m mooted to be sought.