Alberto Malesani is set to take the Genoa post this week.
President Enrico Preziosi took time out to make his final decision on who would replace Davide Ballardini for next season.
Former Palermo tactician Rossi was the favourite for a while, but according to reports over the past few days, he turned down the proposal.
Malesani is a free agent after walking away from Bologna, who he kept in Serie A despite a three-point penalty and the threat of bankruptcy hanging over the club.