While Mauricio Pochettino's men beat Peter Bosz' Dortmund twice in last season's Champions League group stage.
"Teams that are struggling in their league have done very well in the Champions League".
Following the draw, Manchester City remain favourites for the competition according to the bookmakers, while Barca are considered second favourites.
FC Barcelona have been drawn against Olympique de Lyon in the Last 16 of the Champions League.
Champions League last-16 draw: how and where to watch
United, at a low ebb after Sunday's 3-1 defeat to Liverpool, meet PSG for the first time and a formidable task awaits against a side featuring Neymar and Kylian Mbappe - the world's two most expensive players.
Liverpool weren't much better, losing all three away games and this could come to trip them up in the knockout stages.
Well, we asked six of our writers to have their say.
Salihamidzic said, quoted by UEFA.com: "Liverpool are the hottest team right now and top of the Premier League table. Looking forward to it".
Ajax will play the first game at home on the 12, 13, 19 or 20th of February.
"Attractive football, a high tempo - they will be very hard to play against, especially with the second leg in Dortmund, with their fans and the yellow wall, the backing that the crowd gives them there".
Kate reveals Prince Louis has hit an adorable new milestone
As artificial snow fell, William chucked artificial snowballs at a children's entertainer, and Kate was caught in the crossfire. Kate previously wore the chic blazer by the label, which is also one of Meghan's favourites, during her tour of Canada in 2016.
- Mortal Kombat 11 characters revealed with new gameplay screenshots
- Comey set for closed-door interview with House Republicans
- Turkey vows to take on US-backed Kurdish militia in Syria
- Worldwide Markets: Stocks cheered by Trump exchange talk; sterling hooks off lows
- Fortnite season 7 gets snowy, adds planes and a new creative mode
- Trump Nominates Army Chief Milley to Replace Joint Chiefs Chairman Dunford
- Burnley 1-3 Liverpool: Reds mount comeback to ensure record breaking start
- Carbon Emissions Took Off Like a 'Freight Train' in 2018
- Alleged Russian spy Maria Butina cooperating ahead of plea hearing Thursday
- Clippers going all-out with recruitment of Kawhi Leonard, Kevin Durant