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.
There, Jurgen Klopp's men should they advance, will play either Benfica or Marseille. It's AC Milan/Roma v Bayer Leverkusen/West Ham on the other side.
The last-eight ties will be played on 11 and 18 April, with the semi-finals on 2 and 9 May.
The final is scheduled for the Aviva Stadium in Dublin on Wednesday 22 May.
EUROPA LEAGUE 1/4 FINALS
AC Milan v Roma
Liverpool v Atalanta
Bayer Leverkusen v West Ham
Benfica v Marseille
EUROPA LEAGUE 1/2 FINALS
Benfica/Marseille v Liverpool/Atalanta
AC Milan/Roma v Bayer Leverkusen/West Ham
