By SABC Sport
15th March 2024
The sides' only previous encounters were in the Champions League group stage in 2020-21, with the Reds beating Atalanta 5-0 in Bergamo but then losing 2-0 to them at Anfield.
West Ham face a tough challenge against Bundesliga leaders Bayer Leverkusen, who are unbeaten in 37 matches in all competitions this season under their highly-rated coach Xabi Alonso.
Liverpool and West Ham cannot meet until the final in Dublin after the semi-final draw also kept the Premier League teams apart.
The last-eight ties will be played on April 11 and 18, with the final scheduled for Wednesday, May 22.
Aston Villa will go up against French side Lille in the Europa Conference League quarter-finals.
Villa booked their place in the last eight with a 4-0 win over Dutch giants Ajax on Thursday night. The final will be held in Athens on Wednesday, May 29.