Liverpool have drawn Romanians Unirea Urziceni, Everton tackle Sporting Lisbon and Fulham will face Shakhtar Donetsk in the last 32 of the Europa League
Liverpool dropped into the Europa League after being eliminated from the Champions League in the group stage.
Rafa Benitez's men will take on Dan Petrescu's Unirea Urziceni, who were also knocked out of the Champions League in the group stage.
Liverpool could face Lille or Fenerbahce in the last 16 if they successfully overcome the threat of Unirea.
Everton have been handed a difficult draw against Portuguese outfit Sporting Lisbon.
David Moyes' side have the mouthwatering prospect of taking on Atletico Madrid or Galatasaray if they can negotiate the tie with Sporting.
Fulham, who booked their spot in the last 32 with victory over Basle in midweek, have been handed a tricky tie against former Uefa Cup winners Shakhtar Donetsk.
The West London outfit could find themselves up against European titans Ajax or Juventus in the last 16 if they can knock out Shakhtar.
Steve McClaren's FC Twente have been handed a tough tie against Germany's Werder Bremen.
Two former European Cup winners Ajax and Juventus will lock horns in the last 32 after the Italian giants dropped down from the Champions League.
Villarreal have been paired against German champions Wolfsburg, while Atletico Madrid will tackle Turkish giants Galatasaray.