Arsenal also bid €28 million before the World Cup.
However, Sport says Cuadrado's priority is a move to Barca and he and his agent, Alessandro Lucci, will make this clear to Fiorentina directors when they meet later this week.
Fiorentina president Andrea Della Valle would prefer to sell to the highest bidder, but Barca are counting on Cuadrado to make it clear that he'll only leave for the Nou Camp.
Luis Enrique, Barca's new coach, is a big fan of Cuadrado and has made it clear if a deal can be done, he'd be happy to have the Colombian part of his squad next season.
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