The 26-year-old, who has also been linked with Bayern Munich and Arsenal, was co-owned by Firorentina and Udinese before the Viola bought his full sporting rights last month for a reported 15million euros.
Cuadrado is under contract with the Florence-based outfit until June 2017 and the club are hoping to ward off all suitors.
"To keep Cuadrado will be difficult but not impossible," Fiorentina owner Andrea Della Valle said to Gazzetta dello Sport. "I am used to dealing with complicated challenges.
"It's not just Barcelona but there are many others (clubs)."
Cuadrado is currently on holiday after competing for Colombia at the World Cup in Brazil.
The South American star joined Fiorentina two years ago from Udinese and has been a regular in Vincenzo Montella's side, scoring 11 goals and setting up five more in 32 league appearances last season.