Manchester United will face French side Saint-Etienne in the Europa League last 32, while Tottenham Hotspur meet Belgian team Gent.
United midfielder Paul Pogba is set to face older brother Florentin, who plays for the eighth-placed Ligue 1 side.
Spurs have never met Gent, who finished third in the Belgian top-flight last season, in a competitive fixture.
United’s first leg will be played on Wednesday, 15 February, while Spurs play the following day.
The Red Devils will play on Wednesday because Saint-Etienne’s neighbours Lyon are also playing at home in the Europe League that week.
Both return legs will be played on Thursday, 23 February.
The two Premier League clubs could not be drawn together as teams from the same nation are kept apart.
Tottenham, along with the other seeded teams, will be at home in the second leg.
Spurs were seeded after dropping down from the Champions League, while United were unseeded after finishing second in Group A.
But Jose Mourinho’s side are still favourites to win the competition with most bookmakers.
The Europa League final will be held at Stockholm’s Friends Arena on 24 May.
Pogba versus Pogba
Manchester United’s tie with Saint-Etienne will see Paul Pogba face his older brother Florentin, 26.
“It’s nice, it’s a nice thing,” said Mourinho. “Paul will be laughing, and for sure his brother will also be laughing.
“I think it’s nice, it’s happened in the history of football a few times and it’s nice.”
After a group stage that involved a 3,000 mile round trip to Odessa in Ukraine, Mourinho also welcomed a tie that is much closer to home.
“The good thing is the travel,” he added. “We were very unlucky in the group stage, now we go to France.”
Athletic Bilbao (Spain) v Apoel Nicosia (Cyprus)
Legia Warsaw (Poland) v Ajax (Netherlands)
Anderlecht (Belgium) v Zenit St Petersburg (Russia)
Astra Giurgiu (Romania) v Genk (Belgium)
Manchester United (England) v Saint-Etienne (France)
Villarreal (Spain) v Roma (Italy)
Ludogorets (Bulgaria) v FC Copenhagen (Denmark)
Celta Vigo (Spain) v Shakhtar Donetsk (Ukraine)
Olympiakos (Greece) v Osmanlispor (Turkey)
Gent (Belgium) v Tottenham Hotspur (England)
Rostov (Russia) v Sparta Prague (Czech Republic)
Krasnodar (Russia) v Fenerbahce (Turkey)
Borussia Monchengladbach (Germany) v Fiorentina (Italy)
AZ Alkmaar (Netherlands) v Lyon (France)
Hapoel Beer Sheva (Israel) v Besiktas (Turkey)
PAOK (Greece) v Schalke (Germany)