The midfielder is said to have been spotted in a meeting with officials of the Serie A side ahead of possible move this January.
Muntari became a free agent after ending his contract with Saudi Club Al Ittihad.
The 31-year-old will thus be making a return to Italy having featured for Inter-Milan and AC Milan.
Fellow Serie A side Pescara are also in the race for the services of the former Sunderland and Portsmouth ace.
The player could be playing top-flight European football once again should he reach an agreement with Genoa in the coming days.
Despite rendering an apology for his misconduct in the Black Stars team, the UEFA Champions League winner was snubbed by Black Stars Coach Avram Grant ahead of the Africa Cup of Nations in Gabon.