Manchester United will play Club Brugge in the Europa League's round of 32 and Arsenal have been drawn against Olympiacos.
United finished top of Group L and will take on Belgian club Brugge, who failed to qualify for the Champions League knockout phase.
Arsenal's Greek opponents Olympiacos also dropped into the Europa League after finishing third in their Champions League group behind Tottenham.
Wolves have been drawn to play Spanish club Espanyol, Scottish champions Celtic face Copenhagen and Rangers take on Portuguese side Braga.
The first legs of the Europa League round of 32 will take place on 20 February and the second legs on 27 February.
Other notable ties include Getafe against Ajax, Roma versus Gent and Inter Milan against Ludogorets.
Bayer Leverkusen face Porto and fellow Bundesliga side Eintracht Frankfurt will play Salzburg, who finished behind Liverpool and Napoli in their Champions League group.
Ajax, Roma and Inter Milan also failed to qualify for the Champions League knockout phase.
Arsenal club secretary David Miles told BT Sport: "We have played Olympiacos quite a few times.
"We have good friendships. They are one of the best teams in Greece. We know they are strong. We take no-one for granted and will do our homework.
"This could be a route into the Champions League for next year, so I think this will be a priority."