Jupp Heynckes' charges lost the first leg 2-1 at home last week after squandering a number of promising chances to extend their lead following Joshua Kimmich's opener. That result leaves the Bundesliga champions needing a 2-0 win or better in the Spanish capital.
As an impossible a task as that may seem, Hummels insists he and his team-mates are up to the challenge. "Real Madrid are one of the biggest teams in the world and you have to be on your top level to beat them," the 29-year-old said following Bayern's 4-1 triumph at home to Eintracht Frankfurt on Saturday.
"It was possible on Wednesday, even though we didn't play that well. We have to play an extraordinary game to win this thing in Madrid. But it's possible with our team."
Watch: Hummels on the possibility of beating Real Madrid
The Germany international also went on to reiterate his admiration for Real Madrid forward Cristiano Ronaldo: "He's been in good shape for – I don't know – 15 years now. He's incredible. We respect that of course. I think there are a lot of people who admire it and I think they are right in doing so. When it comes to scoring goals he's the best in the world."
Be that as it may, Hummels nevertheless seems to have developed a knack for keeping Ronaldo quiet, his performance at the Allianz Arena last week just the latest in a series of meetings in which the Portuguese has failed to score.
Hummels was part of the Germany team that beat Ronaldo's Portugal in the group stage of the UEFA 2012 EUROs and FIFA 2014 World Cup. He also now faced the Ballon d'Or holder eight times in the Champions League for former club Borussia Dortmund and Bayern (W3, D1, L4).
Hard fought from @fcbayern but they fall to @realmadrid in the first leg 2-1. Still plenty of ⚽️ to play! . . . . #FCB #FCBayern #Munich #miasanmia #Bundesliga #Football #Soccer #Germany #fussball #futbol #goals #lovefootball #thebeautifulgame #instasport #team #soccerislife #footy #skills #matchday #player #match #footballgame #ball
"I watch a lot of the big teams in action, I'm interested in football in general, so there are things you notice," the Bayern defender told SPORT BILD ahead of the first leg, explaining his ability to cope with Ronaldo's threat. "I think there are a couple of patterns with [him], there are certain anomalies. I'll try to make use of what I know, but I’m keeping it to myself.
"Ronaldo has changed his playing style in recent years," Hummels continued. "He's not as dominant as he once was; now he's all about finishing moves off and scoring goals. In that sense, he's the best goalscorer in the world because he can score all kinds of goals, at any point in a game.
"Real are a real threat from the flanks, and from set-pieces with central midfielders like Toni Kroos. You have to defend the balls into the box. That makes it difficult to defend against Ronaldo. He doesn't need eight touches before shooting. He does it with the first or, at the most, the second."
Watch: Mats Hummels answers your pressing questions - against the clock
Bayern travel to Madrid for the second leg on 1 May. The winners will face either Jürgen Klopp's Liverpool or AS Roma in the final in Kiev on 26 May.