Lionel Messi might have scored 40 league goals this season but the Argentinian forward has been a little more subdued in Europe, registering only five times and, more importantly, failing to notch a vital away goal at the San Siro in February.
But Galliani knows the three-time Ballon d'Or winner will be the spearhead of any Barca comeback in the last-16 second-leg clash, while ruing the absence of Milan's own talismanic forward Giampaolo Pazzini.
He told acmilan.com: "We can't go into the game thinking we'll be fine just because we've got a two-goal advantage.
"We are going up against the strongest team in the world who have a monster like Leo Messi who scores all the time. Let's hope he takes it easy on Tuesday night.
"One thing is certain - it will be another great challenge, an infinitely difficult challenge. It's always nice to play Barcelona but we will be going into an incredibly heated atmosphere."
News that Pazzini - who has 13 Serie A goals to his name this term - had suffered a hairline fracture to his fibula during Friday's league win at Genoa was not the confidence boost Milan were looking for.
Galliani remains confident a pool of Stephan El Shaarawy, M'Baye Niang, Robinho and former Barca striker Bojan Krkic will succeed in Catalonia, though.
"It's a shame, a real shame that he's been ruled out," the Milan chief added. "Will we go there to play for him? Yes, for him too.
"We have lost an important striker but whoever replaces him will do well."
The Rossoneri also have concerns over the fitness of French defender Philippe Mexes, who could be replaced by Mattia De Sciglio, but first-leg goalscorers Kevin-Prince Boateng and Sulley Muntari are cleared to start in midfield.
Barcelona's influential midfielder Xavi, meanwhile, has been passed fit after missing the Catalan club's last two games with a hamstring injury.
Barca are unbeaten at home in 19 Champions League matches but the small matter of overturning a two-goal deficit has had varying effects on player morale.
Xavi is optimistic, telling Barca's official website: "We still have 90 minutes, maybe even 120 minutes. A lot can happen in a match.
"We need to be careful, we can't lose possession, we need to avoid giving them any opportunities to counter-attack, we can't commit stupid fouls and our attacks need to have purpose."
When asked if Barca have what it takes to eliminate Milan, though, the Spain international was slightly more cautious.
"Well, it's the Champions League," he added. "Our pride is a bit hurt from the unjust and excessive result from the away leg and we want to recover that sense of winning, of competing, of being a big team.
"There's no better match for that than the one against AC Milan. But we have to attack and score early."
Fellow midfielder Andres Iniesta, however, is convinced Barca's unique spirit of sacrifice will see them through.
The World Cup winner said: "We will make it through to the next round.
"I would put my hand in the fire as many times as I had to for my team. I have absolute confidence that we can do it.
"It will be difficult but not impossible. We have to play this match as it if was a final. That's what our mentality needs to be from the first minute to the last."