The Germany international is happy to take on the Spanish champion or one of the two English representatives.
The Bundesliga outfit beat Zenit St Petersburg 5-4 on aggregate to make it out of the round of 16 and Hummels is now eager to test himself against a team he has not faced before.
"I'd like to play against a team I haven't played against before in the quarters. Maybe Manchester United, Barcelona or Chelsea," Hummels told the official UEFA website. "At the end of the day, though, it doesn't matter who we get – they're all going to be difficult."
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Hummels then reflected on Wednesday's second leg against Zenit and admitted that BVB struggled against the Russian side.
"We're obviously pleased to get through. It's difficult when you know a draw or even a defeat could be enough," he said. "Zenit were a lot better than they were in the first-leg [which they lost 4-2]. I thought Danny in particular had a good game.
"When we went 1-0 down I was thinking: 'Great, that's exactly what we didn't need,' but in the end it didn't matter. Our equalizer calmed us down a bit."