The Serie A club's chief is hopeful that he can persuade the Colombian to ignore advances from the Spanish side, though he accepts the winger may want to move
The 26-year-old helped Fiorentina to a fourth-place Serie A finish last season then starred as Colombia reached the World Cup quarter-finals for the first time in their history.
Barcelona have heavily linked with the player, but the Italian club's chief hopes that Cuadrado can be convinced to stay in Italy.
"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 to fully secure his playing rights, adding to the €6m they are estimated to have already paid over the past two years.