United have enjoyed a drastic improvement in form since the end of the group stages, but take on a PSG side intent on ending their wait for the trophy they covet more than any other.
No-one gave United a hope when this draw was made on December 17.
The Red Devils had just lost back-to-back matches against Valencia and Liverpool and would sack Jose Mourinho the following day with the club 19 points off the Premier League leaders and 11 adrift of the Champions League places.
Now, though, everything has changed and the Ole Gunnar Solskjaer-inspired resurrection has left United with genuine hope of toppling one of the tournament favourites over two legs.
The scale of the turnaround has been quite remarkable, with United having won 10 and drawn one of their 11 matches under Solskjaer so far - most recently a 3-0 triumph over relegation-threatened Fulham on Saturday.
That result saw United climb into the top four, meaning that in the space of less than two months they have enjoyed a 12-point swing which now leaves them one point above both Arsenal and Chelsea.
The latest reports suggest that Solskjaer will be handed the job on a permanent basis, but if there is any remaining doubt in the board's mind then progress into the quarter-finals of the Champions League at the expense of PSG would surely seal the deal.
This will be the Norwegian's first taste of the Champions League proper as a manager, although he is no stranger to the competition in general and memorably scored the 93rd-minute winner in the 1999 final which clinched the treble for United in the most dramatic of circumstances.
United have not reached the quarter-finals of this competition since 2013-14 and crashed out at the hands of Sevilla at this stage last season, where a loss at Old Trafford proved costly.
The Red Devils have now won just one of their last four Champions League home games, although the value of looking back at the Mourinho era for clues as to future form is becoming more and more redundant with each Solskjaer win.
Tuesday's match is likely to be the toughest test Solskjaer has faced yet - and his unbeaten start will surely come under strain during a three-game spell which also sees them take on Chelsea and Liverpool - but United are now playing with the sort of swagger and confidence not seen since the days of Sir Alex Ferguson and will feel as though they can beat anyone at the moment.
Recent Champions League form: WDLWWL
Recent form (all competitions): WWWDWW
The Champions League remains the holy grail for PSG, whose vast expenditure and star-studded lineups are yet to deliver the owners' most coveted prize.
The Parisiens have seen their hopes ended at this stage in both of the past two seasons, incredibly throwing away a 4-0 first-leg lead against Barcelona in 2017 before going down 5-2 on aggregate at the hands of Real Madrid last season.
PSG's hopes in that latter tie were hurt by a season-ending injury to Neymar, and Thomas Tuchel will be hoping that it is not a similar story this time around with the Brazilian once again set for a significant spell on the sidelines.
Edinson Cavani is also expected to miss Tuesday's match to further weaken PSG's attacking threat, so Tuchel will arrive at Old Trafford having battled through a disrupted build-up.
Even the club's domestic form has looked relatively shaky this month, suffering their first league defeat of the season against Lyon, needing extra time to overcome third-tier Villefranche and then scraping past Bordeaux on Saturday.
However, any PSG struggles must be kept in context; they remain 10 points clear at the top of Ligue 1 despite having played two games fewer than second place, and they have only lost three of their 34 matches across all competitions this season.
One of those defeats did come in England as Liverpool ran out 3-2 winners on matchday one of the group stages, but PSG still went on to finish top of a very difficult section which also included Napoli.
Despite that, the French giants have only won three of their last nine matches in this competition, with two of those coming against Red Star Belgrade in this season's group stage.
Indeed, that victory in Belgrade is their only Champions League away win since October 2017, with three defeats and a draw preceding that.
Things may not be as straightforward as many suggested when PSG were drawn against United, then, and the visitors will even go into the game in the unfamiliar position of being underdogs in the eyes of many.
Recent Champions League form: LWDDWW
Recent form (all competitions): WWWLWW
Cavani is a major doubt and unlikely to recover from a hip injury in time to feature in this match, having been forced off at half time of the weekend win over Bordeaux.
Neymar is a longer-term absentee, meaning that Kylian Mbappe will likely be the only member of the usual PSG front three to feature at Old Trafford.
Angel Di Maria could return to his former stomping ground as a result of the injury concerns, with the Argentine having scored three goals in 27 Premier League appearances for United during one unsuccessful season at the club.
United, meanwhile, will monitor the fitness of Victor Lindelof after he missed the win over Fulham due to a knock.
Antonio Valencia, Matteo Darmian and Marcos Rojo remain sidelined for the hosts, but the likes of Marcus Rashford, Jesse Lingard and Ashley Young are pushing for recalls after sitting out at the weekend.
Man Utd possible starting lineup:
De Gea; Young, Smalling, Jones, Shaw; Herrera, Matic, Pogba; Lingard, Rashford, Martial
PSG possible starting lineup:
Buffon; Kehrer, Silva, Kimpembe, Bernat; Marquinhos, Verratti; Nkunku, Di Maria, Draxler; Mbappe
Head To Head
This will be the first ever competitive meeting between these two sides, although they did face each other in an International Champions Cup clash in July 2015 which PSG won 2-0.
United have never lost a home game against French opposition - winning 10 of 13 such outings - and have progressed from six of their seven two-legged ties against Ligue 1 clubs.
PSG, meanwhile, have only ever won one of their 10 visits to English clubs, with that coming in a 2016 victory over Chelsea at this stage of the competition.
We say: Man Utd 2-2 PSG
That United even have a chance of winning this match is testament to how far they have come under Solskjaer already. PSG are missing two of their main men, but they still have quality in abundance and we're backing them to come away with a draw.