The 18-time Italian champions have endured a torrid season by their high standards, and sit 11th in the table with seven games remaining.
Milan have failed to string together a run of more than two Serie A victories in a row, and have lost 11 of their 31 league fixtures this term - meaning they are a mammoth 39 points adrift of table-topping Juventus.
However, an impressive 2-0 triumph at Fiorentina was followed by a comprehensive 3-0 victory over relegation-threatened Chievo last weekend with Mario Balotelli and a double from Kaka - who was celebrating his 300th game for Milan - securing all three points for Clarence Seedorf's men.
Those successes have put Milan back in the hunt for a UEFA Europa League berth, a finish that had looked increasingly beyond their reach.
Milan trail rivals Inter - who sit fifth - by seven points, but another maximum haul at the Stadio Comunale Luigi Ferraris on Monday could further boost hopes of featuring in Europe's secondary competition next season.
Recent history suggests the visitors will triumph, too, with Milan unbeaten against Genoa in the last seven meetings between the clubs, including five victories.
Seedorf has endured an indifferent start to his coaching career at San Siro, yet centre-back Daniele Bonera is confident the team are starting to flourish under the Dutchman's stewardship.
"Seedorf is pretty calm, though of course the defeats affect everyone," he told Sky Sport Italia. "We just needed time to understand get in sync with his ideas.
"Clarence is a coach who likes a certain type of dialogue, so we all needed to just settle in and get to know each other."
Seedorf will be without midfielder Michael Essien for the game, with the Ghanaian sidelined with a thigh problem.
Genoa's recent record against Milan may be unfavourable, but Gian Piero Gasperini's men are just three points and two places below their opponents in the Serie A table.
Moreover, Genoa have proved to be no pushovers at Stadio Comunale Luigi Ferraris, with seven of their 10 league victories this season coming on home soil.
Gasperini's charges had been on course to challenge for a spot in the Europa League at one stage, but a run of just one win in five league matches has dented those hopes.
The reverse fixture at San Siro back in November ended in a 1-1 draw, with former Milan striker Alberto Gilardino equalising Kaka's early opener from the penalty spot.
