However, the 25-year-old, who has been one of the standout players in Serie A this season, has admitted that he wants to "progress and play for big teams".
"Barcelona interest? I've had no contact the Fiorentina have said nothing to me," the Colombian international told el9.cat.
"Every players works to progress and play for big teams, but my mind tells me Fiorentina and I'm very happy here.
"We'll see what happens in the future but I'm only thinking of working hard and developing because I still have room for improvement.
It has been speculated that Barcelona are keen to use Cuadrado as an attacking right-back.