Saudi Arabian clubs and Serie A newcomers Monza are also in contention for the veteran defender.
Acerbi made 18 league appearances this season, starting 15, as Inter Milan won the Serie A title by 11 points from Napoli — a fourth successive Scudetto for the Milan club. Despite his age, his ability to read the game, organise defensive lines and distribute from the back has sustained his usefulness in Cristian Chivu's squad throughout the campaign.
Genoa, who survived Serie A with a 16th-place finish, regard Acerbi as a cost-effective defensive reinforcement at a known quality level — someone who can improve their backline without requiring a significant transfer investment. A low-cost or free arrival aligns with the club's summer planning.
There is also reported interest from Monza, who were promoted back to Serie A and will compete in the top flight for the third time in their history. Both Italian options offer continuity at the highest domestic level.
Acerbi joined Inter from Lazio in 2023 and has previously spent extended spells at Sassuolo and the Rome club. He has earned 34 senior caps for Italy, scoring one goal and providing one assist.