The Viola are just back from their South American jaunt, which saw them visit Argentina, Brazil and Peru.
Coach Vincenzo Montella named his squad for the next pre-season stage, which will take place in Spain, and Cuadrado has been included despite being at the centre of a supposed bidding war between Manchester United and Barcelona.
His presence suggests Fiorentina still have hope of keeping him for another year.
Also included in the squad are Matias Vecino and Rafal Wolski, who are reportedly on the verge of joining Empoli on loan.
Federico Bernardeschi has been left behind in Italy, as he was diagnosed with tonsillitis this weekend.
Fiorentina squad for Spain tour: Alonso, Brillante, Cuadrado, Gomez, Hegazi, Iakovenko, Ilicic, Babacar, Lazzari, Lezzerini, Mancini, Neto, Pasqual, Piccini, Gonzalo, Roncaglia, Rossi, Joaquin, Savic, Tatarusanu, Tomovic, Borja Valero, Vargas, Vecino, Wolski, Aquilani, Pizarro
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