The 26-year-old, who was ever-present at the World Cup as Colombia reached the quarter-finals, is reported to be a target for Barcelona, Bayern Munich and Arsenal among a host of other European clubs.
Cuadrado joined Fiorentina from Udinese in 2012 and has established himself as a key figure for the Viola, hitting 11 goals and assisting five in 32 Serie A outings during the last campaign.
Montella told Sky Sport Italia: "Should he stay, it will be good. Otherwise, we will seek to replace him.
"We need to evaluate the player's aspirations and, above all, if there is a club out there that can pay what he is truly worth."
Meanwhile, Cuadrado's former Fiorentina team-mate, Stevan Jovetic, has hailed the Colombian and believes he would be a good fit for Manchester City.
When asked during a Q & A session who he would recommend to City, Jovetic replied: "So many good players! I like maybe Cuadrado from Fiorentina. He's a very good player, I played with him and also he's a good guy."