The Della Valle family - owners of luxury goods maker Tod's - saved the club in 2002 after it was demoted to the fourth tier due to bankruptcy.
On Monday, the Della Valle family published a statement on the club's official website declaring their willingness to sell should the right offer present itself.
"ACF Fiorentina's ownership announces it is absolutely available, given the dissatisfaction on the part of the supporters, to stand aside and put the club at the disposal of those who want to buy it in order to manage it as they feel is right," the statement read.
"This is the time when those who love the purple jersey and believe the club can be managed differently and more successfully must come forward.
"The owners are available to welcome concrete offers, obviously only by those who really love the purple jersey and have the seriousness and solidity necessary to drive a demanding club such as Fiorentina."
Fiorentina, which finished eighth in Serie A last season.