Double cash plus player offers have been declined by the Italian outfit who only want a straight €15 million for the Italy international
Genoa, who have long been linked with the 29-year-old, are said to have offered €8 million plus the full rights of midfielder Houssine Kharja.
Marseille made an unknown bid that included the full rights of Lucho Gonzalez, who is set to leave France this summer.
However, Fiorentina turned both offers down. The Tuscan club are not opposed to selling Gilardino, but they want at least €15m for the striker.
Gilardino joined his current club in 2008, but caused controversy last season when he questioned the long-term ambition of the Artemio Franchi outfit.