Fulham face Europa holders Shakhtar
Ajax Amsterdam and Juventus, European champions six times between them, were thrown together in Friday's draw.
AS Roma were handed a difficult tie against Greek side Panathinaikos and Bundesliga champions VfL Wolfsburg, who were eliminated from the Champions League after losing their final two group games, were pitted against Spain's Villarreal.
Austrian club Salzburg, the only team to complete the Europa League group stage with a 100 percent record, will face Belgium's Standard Liege.
Ajax have been European champions four times - including three successive wins from 1971-73 - and Juventus twice.
The Italian side were eliminated from the Champions League when they lost 4-1 at home to Bayern Munich in their final game.
Fulham or Shakhtar await the victors of the competition's stand-out tie, while Lille or Fenerbahce will play Liverpool or Unirea Urziceni in two of the highlights of the last 16 draw also made on Friday.
Draw for the Europa League last 32 and last 16 rounds made in Nyon, Switzerland on Friday.
Rubin Kazan (Russia) v Hapoel Tel Aviv (Israel)
Athletic Bilbao (Spain) v Anderlecht (Belgium)
FC Copenhagen (Denmark) v Olympique Marseille (France)
Panathinaikos (Greece) v AS Roma (Italy)
Atletico Madrid (Spain) v Galatasaray (Turkey)
Ajax Amsterdam (Netherlands) v Juventus (Italy)
Club Bruges (Belgium) v Valencia (Spain)
Fulham (England) v Shakhtar Donetsk (Ukraine)
Liverpool (England) v Unirea Urziceni (Romania)
Hamburg SV (Germany) v PSV Eindhoven (Netherlands)
Villarreal (Spain) v VfL Wolfsburg (Germany)
Standard Liege (Belgium) v Salzburg (Austria)
Twente Enschede (Netherlands) v Werder Bremen (Germany)
Lille (France) v Fenerbahce (Turkey)
Everton (England) v Sporting (Portugal)
Hertha Berlin (Germany) v Benfica (Portugal)
Hamburg SV/PSV Eindhoven v Athletic Bilbao/Anderlecht
Rubin Kazan/Hapoel Tel Aviv v Villarreal/VfL Wolfsburg
Atletico Madrid/Galatasaray v Everton/Sporting
Hertha Berlin/Benfica v FC Copenhagen/Olympique Marseille