Massimiliano Allegri's men have endured a dreadful start to the season and sit 19 points behind league leaders Roma in 10th.
Milan have not tasted victory in any competition since their 1-0 home win over Udinese on October 19.
However, their recent form against the Ligurian outfit has been impressive, with Milan winning five of the last six encounters between the two sides.
The hosts 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 together 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 head coach Gian Piero Gasperini's return to the Stadio Luigi Ferraris.
The visitors have lost just once since Gasperini's appointment on September 29, and sit seventh in Serie A as a result.
Gasperini's side have not conceded a goal in three games and will be hopeful of maintaining their strong defensive record against a Milan side that has struggled to find the net in recent times.
Defender Alessandro Gamberini (back) is unavailable for Genoa, however, as is striker Ze Eduardo (hamstring).
Despite those absences, right-back Sime Vrsaljko is confident Genoa can continue their fine form.
"We're expressing ourselves well at Genoa and playing good football," he told the club's official website.
"Gasperini and the results have brought enthusiasm, trust and determination. We want to defend our seventh-place position and give satisfaction to the fans."
