The tie will see Pogba, the world's most expensive player, come up against his elder brother Florentin.
Manchester United will take on Saint-Etienne in the last 32 of the Europa League, with Jose Mourinho's side hosting the French club in the first leg, after Monday's draw.
The tie will see United and France midfielder Paul Pogba, the world's most expensive player, come up against his elder brother Florentin, the Guinea international defender.
"That's a nice thing," said Mourinho at a press conference on Monday. "Paul was already laughing about it and for sure his brother is also laughing.
"It has happened a few times in the history football and it's a nice thing."
The teams met in the now defunct Cup Winners' Cup first round in 1977, with United winning 3-1 on aggregate.
On that occasion, United were forced to host the second leg in the southern English city of Plymouth, 450 kilometres away, following crowd trouble in the first leg in France.
Mourinho's men finished second in Group A behind Fenerbahce of Turkey while Saint-Etienne topped Group C. After also having to go to Ukraine to face Zorya Luhansk in the group stage, United's Portuguese manager is pleased that there will be no long away trip this time.
"The good thing is the travel distance. We were very unlucky in the group phase, we had to go very far, it was very difficult to go to Turkey, Ukraine," he said.
"Now we go to France because the flight is easy and it's not an easy period, there are lots of games, so that is good."
Saint-Etienne, 10-time French champions and European Cup runners-up in 1976, are currently eighth in Ligue 1.
"Saint-Etienne is an historic old club with lots of tradition. People of my generation will never forget that (Michel) Platini team and it will be difficult because every team now is a good team in the competition.
"For sure, Manchester United is one of the big names in the competition but we have two months without the Europa League, two months to forget it, then we will see."
The other Premier League representative, Tottenham Hotspur, will face Gent of Belgium after being eliminated from the Champions League at the group stage.
Villarreal of Spain will face Italian giants Roma in one of the standout ties, while Bundesliga club Borussia Moenchengladbach were drawn against Fiorentina of Italy.
The first legs will be played on Thursday, February 16, with the return matches a week later.