The 26-year-old has been heavily linked with a big-money move away from Serie A since his impressive showing at the World Cup, with Barca and United most strongly credited with an interest.
Reports in Spain earlier this week claimed that Barca were looking to the player to pressure Fiorentina into allowing him to leave, in a similar manner to how Jeremy Mathieu forced a move from Valencia to the Nou Camp earlier this month.
Fiorentina, though, have made clear the figure they want before they consider allowing Cuadrado to leave.
Sporting director Daniele Prade told Sky Sport 24: "If we received an offer of 50 million euros (£40million), we would sit down and talk. But we haven’t received that offer.
"We hope Cuadrado stays with us. There are no formal offers and we are in constant contact with the player and his agent. On August 4 or 5 he has to be back, and then we will talk.”
The player's agent Alessandro Lucci insists that he is not in talks with any club, but admits he has spoken to Barcelona.
"I have been in direct contact for time with Barcelona and other clubs. There are expressions of interest but to date there is no negotiation ongoing, neither with Barcelona nor with any other outfits.
"The Catalan club is represented by serious and professional people who has never asked us to put pressure on Fiorentina.
"With Fiorentina my personal and professional relationship is very positive and the Cuadrado's one is the same. If there were to be an important and top-level negotiation, it will be analysed and if necessary finalise it together. "