With neighbours Manchester City running away with the Premier League title, this represents United's last chance of winning a trophy this season.
Mourinho has made himself an unnecessary target with his overly-cautious approach to the two legs against Sevilla, and Red Devils supporters will start asking serious questions of his suitability if they follow their European setback by crashing out to Brighton.
Second place in the Premier League, consolidated by last weekend's 2-1 win over Liverpool, may not save Mourinho from scrutiny when the club's two fiercest rivals are playing the sort of expansive football which is usually synonymous with United themselves.
United's legacy is built on attacking football which wins trophies and while the Special One has a brilliant record for sniffing out silverware, he has not fared as well in the FA Cup as he has other competitions, lifting the trophy only once courtesy of a victory over United in the 2006-07 final during his first spell as Chelsea manager.
The North-East giants did win the competition as recently as 2016 in Louis van Gaal's last match at the helm before Mourinho's arrival, although that was only the club's second FA Cup triumph since the turn of the century.
The defeat to Sevilla was just United's second of the season at Old Trafford, the other being at the hands of Man City in December, so Mourinho should find solace in home comfort on the back of Tuesday's surprising result.
However, the atmosphere inside the stadium will be anything but comfortable if Mourinho persists with his pragmatic tactics against Brighton as there is no excuse for the Red Devils not to take the game to Chris Hughton's side.
While the Portuguese might point to the fact that United have scored eight goals in their last four matches, they have only scored four goals in a game once since November, having done it eight times in the opening months of the season, which is proof that Mourinho has fallen back into old habits.
Recent FA Cup form: WWLWWW
Recent form (all competitions): WDWWWL
Three wins from their last five Premier League games have lifted Brighton to a dreamy 11th in the table, seven points above the relegation zone which should give Hughton the freedom to have a real go at the FA Cup too.
With the international break coming up and the fixture on their return being a throwaway trip to the Etihad Stadium, Hughton has the luxury of going with a full-strength lineup rather than a rotated side as he has in previous rounds.
The Seagulls have knocked off rivals Crystal Palace, Middlesbrough and Coventry City on their way to their first quarter-final in 32 years, with 13-goal top scorer Glenn Murray notching late winners on a couple of occasions.
Brighton and Murray fired their first blank in eight matches last Saturday when they were beaten 2-0 by Everton at Goodison Park, and his side's away form will be one of few concerns on Hughton's plate ahead of the run-in.
Only once since November have the Eagles tasted victory on the road, and that was against Championship Boro in this competition.
However, the Premier League rookies gained a massive confidence boost recently when they beat Arsenal 2-1 at the Amex Stadium, which proved that they can go toe-to-toe with the biggest clubs, after previously failing to take a single point off top-six opposition this season.
Should Albion produce another elite scalp this weekend to book a Wembley semi-final date, and go on to secure their top-flight safety, then Hughton would arguably put himself in the frame for Manager of the Year honours.
Recent FA Cup form: LWLWWW
Recent form (all competitions): WDWWWL
Paul Pogba could be recalled having being left on the bench for the defeat to Sevilla following a recent injury concern; his failure to start again could suggest a lack of trust or harmony in his relationship with Mourinho.
Injuries to Marcos Rojo and Phil Jones mean that Eric Bailly may start for the third time in a week, shortly after returning from a three-month layoff. Victor Lindelof is on standby if the Ivorian's fitness is seen as a potential risk.
Anthony Martial and Juan Mata are both pushing for starts, and it was the guile of the Spaniard rather than the pace of the Frenchman which was missing at Old Trafford in midweek so he could come in at the expense of Jesse Lingard.
Brighton are without Anthony Knockaert after the winger's petulant red card against Everton, which could give Solly March the opportunity to play in behind the lone striker. Although Murray has been in fine form, Hughton will be keen to give record signing Jurgen Locadia another outing after his goal in the last round.
The Seagulls are sweating on the fitness of midfielder Dale Stephens, who sat out on Merseyside, while Gaetan Bong is another injury doubt. Beram Kayal and Markus Suttner are likely to be the beneficiaries if Hughton is not at full strength.
Man Utd possible starting lineup:
De Gea; Valencia, Bailly, Smalling, Young; Matic, Pogba; Rashford, Mata, Sanchez, Lukaku
Brighton possible starting lineup:
Ryan; Schelotto, Dunk, Duffy, Suttner; Gross, Kayal, Propper, Izquidero, March, Locadia
Head To Head
The Red Devils have won their last three matches against Brighton, all by a 1-0 scoreline although it took a Lewis Dunk own goal to separate the sides at the Theatre of Dreams in November when the Seagulls put up a real fight.
Brighton's last victory over United came in 1982 at the old Goldstone Ground in Hove, and they have never won at Old Trafford or beaten them in six attempts in the FA Cup.
The Seagulls' most memorable clash with the 12-time winners came in the 1983 final when they were beaten 4-0 in a replay after rescuing a draw from the original tie at Wembley through a 87th-minute Gary Stevens equaliser.
The teams have faced each just once in the competition since, when a young Ryan Giggs knocked Brighton out in the fourth round 10 years later.
We say: Man Utd 2-0 Brighton
If this game were at the Amex then Brighton might fancy their chances of unsettling United even further, but the Red Devils are usually so commanding at home and Mourinho is not going to let another trophy slip through his hands easily.
Romelu Lukaku has been in fine form of late and usually eats teams like Brighton for breakfast, while Alexis Sanchez is due a performance having been largely underwhelming since his high-profile move from Arsenal in the January window.