Despite the heavy competition with the best midfielders in that time such as Zinedine Zidane, Costa was named the best number 10 player in Serie A a few times. His departure from Fiorentina was discussed every season, since many clubs constantly showed interest in signing him. However, he only left Fiorentina one season before their bankruptcy in the 2001–02 season. With the Florentine club, Costa won the Coppa Italia twice, also winning a Supercoppa Italiana. In June 2001, Fiorentina agreed to sell both Costa and Francesco Toldo to Parma for 140 billion lire. Despite both players refusal to join, Costa and Toldo were sold to AC Milan and Inter Milan, respectively, for the same total transfer fee.