The Colombia winger has been linked with a move to the Premier League title-chasers in the January transfer window and reports claimed that he attended their League Cup draw with Liverpool at Anfield on Tuesday as a guest of the Blues' kit manufacturer.
Jose Mourinho professed to know nothing of such a visit, however, from the 26-year-old, who only completed a switch to full ownership by the Tuscan club in 2014.
Cuadrado underlined his value to Fiorentina with a penalty in the 3-1 Coppa Italia victory over Atalanta on Wednesday, sending his side into the quarter-finals in a game which also saw Mario Gomez score twice to break his goal drought.
And Montella told the press afterwards: "To date, there is no chance that Cuadrado leaves Fiorentina.
"He knows that some things are exaggerated."