The Reds came through an all-Premier League quarter-final against Manchester City, winning the first leg 3-0 at Anfield and the second 2-1 at the Etihad Stadium.
Serie A side Roma produced a remarkable comeback to knock out Barcelona. The Italian team lost the first leg 4-1 in Spain, but progressed on away goals following a 3-0 home victory.
The other semi-final will be between European heavyweights Bayern Munich and holders Real Madrid, who needed a dramatic stoppage-time penalty from Cristiano Ronaldo to see off Juventus after the Italian outfit had come back from 3-0 down in the first leg to level the tie.
Bayern are at home first out against Real on Wednesday 25 April, with the return leg the following Tuesday.
Shortly before the draw, Bayern announced that former player Niko Kovac will become the club's next head coach.
Croatian Kovac is currently boss of Eintracht Frankfurt but will leave that position at the end of the season.
Bayern have been led by interim boss Jupp Heynckes since October, following the sacking of Carlo Ancelotti. They clinched the Bundesliga title last Saturday with a 4-1 win against Augsburg.
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