Liverpool were drawn against Italian side Atalanta in the last eight of the Europa League.
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 at Anfield.
West Ham face a tough challenge against German league 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.
Europa League draw
- Quarter-finals: AC Milan v Roma, Liverpool v Atalanta, Bayer Leverkusen v West Ham, Benfica v Marseille
- Semi-finals: Benfica or Marseille v Liverpool or Atalanta, AC Milan or Roma v Bayer Leverkusen or West Ham
- Liverpool - 10/11
- Bayer Leverkusen - 7/2
- AC Milan - 13/2
- Roma - 12/1
- West Ham, Atalanta - 16/1
- Benfica - 18/1
- Marseille - 20/1
Villa to face Lille
Meanwhile, in the Europa Conference League, Aston Villa were drawn against French side Lille.
Should Unai Emery's side, who made light work of Ajax in the last 16, progress they will face Olympiakos or Fenerbahce in the semi-finals.
Conference League draw
- Quarter-finals: Club Bruges v PAOK, Olympiakos v Fenerbahce, Aston Villa v Lille, Viktoria Plzen v Fiorentina.
- Semi-finals: Aston Villa or Lille v Olympiakos or Fenerbahce, Viktoria Plzen or Fiorentina v Club Bruges or PAOK.
Odds correct at 1330 GMT (15/03/24)
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