The Reds confirmed their passage to the competition’s last four with a 3-3 draw against Benfica at Anfield on Wednesday night that completed a 6-4 aggregate victory.
Villarreal, meanwhile, had sealed their place in the semi-finals with a 1-1 draw at Bayern Munich on Tuesday, clinching the tie 2-1 on aggregate.
Liverpool will be at home for the opening leg of the semi-final, on either April 26 or 27, with the return game to be played at Estadio de la Ceramica on May 3 or 4.
The sides’ only previous meetings came at the same stage of the 2015-16 Europa League, when Jürgen Klopp’s team were 3-1 winners on aggregate.