Gasperini spent four years as Genoa boss in a successful spell, leading the club to promotion and a fifth-placed finish in Serie A - their highest position in nearly two decades.
Preziosi has decided to act after a poor start to the campaign for the Rossoblu, which has seen Fabio Liverani's side win just one of their first six league games.
Liverani was given his first coaching job by Preziosi during the close season but is under extreme pressure to improve results already.
After last night's 2-0 home defeat to Napoli, the Genoa president had dinner with Gasperini and reportedly agreed a one-year contract to make him the club's new coach, according to Football Italia.
Since leaving Genoa in 2010, Gasperini has failed to find a long-term position, with spells at both Inter Milan and Palermo ending abruptly.