The 21-year-old striker has emerged as a much-wanted young attacker in Europe after scoring 21 Serie A goals last season.
His future has been under the scanner this summer with several clubs firm admirers of his abilities, including Liverpool, who explored a deal earlier this year.
Tottenham are believed to be interested in signing the Serbian and Inter are considering him as the replacement for Romelu Lukaku if he joins Chelsea this summer.
Fiorentina are clear about holding on to him beyond the end of the transfer window, but according to Italian daily Il Corriere Fiorentino, the club do have a pain threshold.
It has been claimed that Fiorentina could be forced into making a decision on him if they received a bid worth €60m for Vlahovic.
The striker has been preparing calmly during pre-season but a big offer could turn his head this month.
However, his suitors are running out of time to make a move as Fiorentina are in advanced negotiations with the striker over a new deal.
And it has been claimed that the two sides are very close to reaching a final agreement over the new contract.