Atletico Madrid are pushing to land the striker this summer and have offered a deal worth €50m plus another €10m and a 20 per cent sell-on clause.
But Fiorentina are not prepared to accept the offer and are working towards keeping Vlahovic at the club this season.
Tottenham are also interested in the 21-year-old forward, but it is unclear whether they can stump up the cash for him without selling Harry Kane.
However, Paratici is a big admirer of Vlahovic and will continue to keep tabs on him if he fails to sign him.
The Tottenham football managing director will try and get his hands on Vlahovic again next summer and is already laying the groundwork, establishing good relations with the player’s camp.
Spurs have not made an official bid for him but they have a strong interest in a striker who scored 21 goals in Serie A last season.
Fiorentina have offered him a new contract, which club president Rocco Commisso has claimed is the most expensive contract in their history.
Commisso also recently said that he cannot turn his back on eye-watering offers for Vlahovic if he receives them.
