The 25-year-old Colombia international is co-owned by Fiorentina and Udinese, and joined the Viola in 2012 after finding his opportunities limited in Udine following his switch from Independiente Medellin in 2009.
He has played seven times for the Viola this term, including scoring in Thursday's 3-0 Europa League victory over Pandurii.
Despite being linked with a move away, Cuadrado is concentrating solely on events on the pitch.
Speaking after the match, he said: "The rumours about my future? I am very happy here in Fiorentina and I think only of playing a great championship in this shirt.
"When this season ends we will see everything, but for now I don't want to think about the (transfer) market."