The Rossoneri will join Juventus in the last eight of Europe's premier competition if they can protect a two-goal advantage at Barcelona on Tuesday night.
Allegri, however, is more concerned with keeping resurgent Genoa at bay on Friday night, with Inter Milan, Lazio and Fiorentina all poised to capitalise should the Rossoneri stumble.
The Milan boss told his club's official website: "We can't relax because there are a lot of teams close to us who we still have to go up against.
"The plan is to move forward in the championship and if we don't get through to the next round of the Champions League, then we've done well regardless.
"We have to defend our current position so that we can at least make next season's qualifiers.
"Between now and the end of the season, we have to maintain our current form and make the most of these two months with great enthusiasm."
Two of Milan's closest challengers go head-to-head on Sunday night as Lazio welcome Fiorentina to the Stadio Olimpico.
The Biancocelesti have slipped out of the top three after recording just one win from seven games, while Fiorentina remain in touch having beaten Chievo last time out.
Lazio goalkeeper Federico Marchetti dismissed recent criticism of his side's poor run, telling La Repubblica: "These kind of things make me laugh.
"We are just experiencing a little bit of psychological burnout based on the tough games we had in the first round of fixtures."
His Fiorentina counterpart, Emiliano Viviano, is more optimistic, saying: "In April we can start thinking about Europe.
"Even though we are a few points away from the Champions League places, we will have a go."
There is no respite for league leaders Juventus, who booked their place in the last eight of the Champions League at the expense of Celtic, as in-form Catania visit Turin looking to atone for a dramatic home defeat to Inter.
The Nerazzurri return from a Europa League meeting with Tottenham to face the challenge of an improving Bologna team, while second-placed Napoli strive to end a debilitating run of four consecutive draws when they visit lowly Chievo.
Roma striker Francesco Totti, meanwhile, can become the second highest all-time goalscorer in Serie A if he finds the back of the net at Udinese, after the veteran matched Gunnar Nordahl's tally of 225 goals with a penalty against Genoa.
The picture at the other end of the table is becoming clearer ahead of the run-in, with Palermo welcoming Siena to the Renzo Barbera for a relegation six-pointer after bottom side Pescara take on Atalanta in Bergamo.
The Delfini are under new management in the wake of Cristiano Bergodi's sacking, with former youth-team coach Cristian Bucchi tasked with overhauling a five-point deficit and securing survival.
Elsewhere, struggling Parma bid to seal a first win in nine at the expense of Torino while mid-table Sampdoria take on Cagliari at the Stadio Is Arenas.