Real Madrid drew Juventus in a repeat of last season's final, while Barcelona meet Roma and Sevilla play Bayern Munich. In the Europa League, favourites Atlético Madrid were paired with Sporting CP.
The three Spanish clubs in the hat avoided each other in Friday's Champions League quarter-final draw in Nyon, but the Premier League's two remaining representatives will face off.
Holders Real Madrid will take on Juventus in a repeat of last season's final, while Barcelona were handed a clash with the other Italian side in the draw, AS Roma.
Fresh from sensationally dumping out Manchester United in the round of 16, Sevilla were given a tough last-eight tie with five-time winners Bayern Munich.
And in the competition's first all-English match-up since 2010/11, Liverpool will meet Manchester City.
Champions League quarter-final draw in full:
Barcelona vs Roma
Sevilla vs Bayern Munich
Juventus vs Real Madrid
Liverpool vs Manchester City
Sevilla vs Bayern and Juventus vs Real are to be played on 3 and 11 April, while Barça vs Roma and Liverpool vs City will take place on 4 and 10 April.
In the draw for the Europa League quarter-finals, meanwhile, the only LaLiga team left in the tournament, favourites Atlético Madrid, were pitted against Portugal's Sporting CP.
Europa League quarter-final draw in full:
RB Leipzig vs Marseille
Arsenal vs CSKA Moscow
Atlético Madrid vs Sporting CP
Lazio vs RB Salzburg
The first legs will be held on 5 April, with the ties then decided seven days later.
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