According to reports in Spain, the Catalan club remain keen on the Colombian as they believe he can replace Dani Alves.
However, Barcelona’s move for Cuadrado depends on the outcome of their appeal over a two-year transfer ban to the Court of Arbitration of Sport.
FIFA agent Francois Gallardo: “The player will leave Barcelona next season. He has signed a preliminary agreement with Manchester United.”
If both clubs decide to pursue Cuadrado next summer then they will likely have to meet a £40m asking price as he is set to extend his Fiorentina contract.
Talks have been held in recent weeks over a new deal and La Viola sporting director Daniele Prade is confident an agreement will be struck.
He said: “We’re negotiating.
“Both parties are discussing the situation and we want to do everything with the greatest serenity for everyone involved. We are hope to soon find a point of agreement.”