Cuadrado, 26, has been linked with a move to Manchester United and Barcelona in the coming weeks after impressing with his nation at the World Cup in Brazil this summer.
And despite his best efforts to try and change the player's mind, Della Valle fears he has lost his battle to keep him in Florence.
"I spoke with Cuadrado and I have presented our project [to him],” Della Valle told Italian publication La Gazzetta dello Sport.
“I told him to stay another year in the team with a winning project. But, I am not optimistic because he has received important offers and we may have to let him go.”
When asked if a deal with a prospective club was close, Della Valle said: "We'll see what happens over the next week.
“The boy had a good reaction. We spoke discreetly. It was a clear negotiation with the player. The World Cup that he played in [with Colombia] has not helped.”
He added: “Juan is a very discreet guy and honest.”
Della Valle confirmed that Cuadrado’s future would be sorted within “a maximum of two weeks” with the 26-year-old's transfer fee in any prospective deal expected to be between €40 million and €50 million.
His current deal with Fiorentina runs until June 2017.