Fiorentina general manager Sandro Mencucci is unhappy with fans' protests against the club's owners.
The Della Valle brothers still run the club, but do not have a day-to-day connection that a President requires.
"I hope Andrea Della Valle returns to the role, but I don't know if more work with the family business will allow him to do that," said Mencucci.
"Giancarlo Antognoni? He is a figure we all respect very much, but a President is not just for image."