Andrea Della Valle, Fiorentina co-owner, has conceded that his club faces a real battle to keep hold of its star asset, after Cuadrado starred at the World Cup for Colombia.
Liverpool, Manchester United, Spurs and Arsenal lead a group of clubs across the European continent keen on signing the winger, according to the Daily Star.
Difficult, not impossible
But while Della Valle admits Fiorentina face a challenge resisting bids for the 26-year-old, he insists it's not an impossible task.
"To keep Cuadrado will be difficult but not impossible," said Della Valle. "I am used to dealing with complicated challenges. It's not just Barcelona but there are many others [clubs]."
Depending on the report you read, Cuadrado is valued at anywhere between £20m and £30m by his Serie A club. He ended a successful season last term with 11 goals and five assists from 32 league appearances, which included a stunning run of form towards the end of the campaign when he bagged six goals in the final seven games of the season.
And he carried that form into the World Cup, scoring one and providing four assists as Colombia reached the quarter-finals, only to lose to Brazil 2-1.
As is often the case, the hottest names from the World Cup become the most in-demand, and often as a result the most overpriced, transfer targets of the summer.
Arsenal can probably be ruled out now having splashed out on Chilean winger Alexis Sanchez, but Manchester United, Tottenham and Liverpool all have money to spend.
Especially Liverpool, who today confirmed they have reached an agreement for the sale of striker Luis Suarez to Barcelona.
Reports claim the transfer fee is likely to range between £63m and £75m for the Uruguayan international, who is banned from football related activity for four months after his bite at the World Cup.