The Serie A club's chief is hopeful he can persuade the Colombian he can ignore transfer overtures, though he accepts he might already have his heart set on a departure.
The Colombian, 26, helped Fiorentina to a fourth-place Serie A finish last season then starred as his national team reached the World Cup quarterfinals for the first time in its history.
Barcelona has been rumoured to be desperate to sign him as Dani Alves' successor, but the Italian club chief is holding on to the slender hope that Cuadrado can be convinced to stay at the Artemio Franchi.
"When Cuadrado returns we want to see if he shows us the desire to stay at Fiorentina," Della Valle told Radio Blu. "If he really does want to remain then we will talk to him and be honest about resolving the situation.
"It’s complicated, but not impossible. I’ll do everything I can to keep him, even if requires making sacrifices elsewhere, but if Cuadrado is no longer motivated to stay here then we can only accept that and move on.
"However, at the moment I don’t get that vibe from him."
Cuadrado has been with Fiorentina since 2012 but was co-owned with Udinese until last month when the Viola paid 15 million euros to fully secure his playing rights, adding to the €6m they are estimated to have already paid over the past two years.