The Colombian international has impressed in Serie A this season and is winning admirers all over Europe.
At present Cuadrado's rights are co-owned by Fiorentina and Udinese, but it has been reported that the two clubs have agreed a deal for the Viola to buy out Udinese's share in the summer.
Once Fiorentina own Cuadrado fully they will be able to listen to offers from other clubs with German giants Bayern Munich said to be interested.
Arsenal have repeatedly been linked with the 25-year-old and in recent weeks Manchester United are said to have joined the chase as they look to rebuild in the summer.
Fiorentina will be reluctant to let such a pivotal figure leave, but coach Montella knows that the Tuscans don't have the financial resources to resist.
"I'd like Cuadrado to stay in Florence, that seems pretty obvious, but there could be an offer the club and the player can't refuse," Montella is quoted as saying by Tuttosport.
The paper insists that representatives of the two clubs could have discussed Cuadrado over dinner when they met in the Europa League and that Antonio Conte is a fan of the winger who would allow him to play 4-3-3.