Massimiliano Allegri's side haw made a terrible start to the season and needs three points to relieve the pressure on its under-fire coach.
Massimiliano Allegri's men have endured a dreadful start to the season and sit 19 points behind league leader Roma in 10th.
Milan has not tasted victory in any competition since a 1-0 home win over league rival Udinese on October 19, but the club's recent form against Genoa has been impressive, with the Rossoneri winning five of the last six encounters.
The home side will attempt to continue that run without a number of key players, among them suspended captain Ricardo Montolivo.
Striker Mario Balotelli returns from his ban, but Stephan El Shaarawy (foot) and Antonio Nocerino (calf) are likely to miss out, along with Giampaolo Pazzini, Marco Amelia (both knee) and Mattia De Sciglio, while Cristian Zaccardo (ankle) is doubtful.
Genoa's upturn in fortunes has coincided with coach Gian Piero Gasperini's return to the Stadio Luigi Ferraris, losing just once once since the appointment of the former Inter boss on September 29.
The seventh-placed side has not conceded a goal in three games either and will be hopeful of maintaining its strong defensive record against a Milan side that has struggled to find the net in recent weeks.
Defender Alessandro Gamberini (back) is unavailable for Genoa, however, while striker Ze Eduardo (hamstring) is also out.