The Reds have been drawn against Belgian side RSC Anderlecht with a place in the last four of the competition at stake.
United edged through to the quarter-finals with a slender 2-1 aggregate win over Rostov after Juan Mata's solitary goal at Old Trafford.
As with the last 16 tie against the Russians, the two-legged contest is sandwiched between a heavyweight meeting with Chelsea.
With tournament favourites Roma and Monchengladbach now out of contention, Jose and the team are now the clear front-runners to go on and lift the trophy in May's Stockholm final.
The first leg will be played at the Constant Vanden Stock stadium on 13 April with the return at Old Trafford a week later.
Anderlecht's elimination in the Champions League third qualifying round pushed them into Europe's second tier tournament.
On route to the clash against the Reds, they finished second in Group C before they edged past Zenit Saint Petersburg on away goals.
They saw off Cypriot outfit APOEL Nicosia (2-0 on aggregate) in the round of 16 and currently lead the standings in their domestic league ahead of Club Brugge.
Even though matches between the two sides have been few and far between, Anderlecht hold a unique place in United's history.
The Belgians provided the opposition for the Reds first ever foray into European competition back in 1956.
The "Busby Babes" won 2-0 in Belgium before, most famously, Anderlecht found themselves on the end of the Reds record scoreline - a 10-0 win in the second leg at City's Maine Road ground.
The sides next meeting came in November 1968 when United were holders.
A 3-0 win at Old Trafford proved just enough for the Reds to go through on aggregate despite a 3-1 defeat in the away match.
Anderlecht also won the last meeting at their place, 2-1 in the group stage in the 2000-01 season, but we avenged that defeat with a 5-1 thumping at Old Trafford in the return.
Of the sides left in this year's tournament, Lyon look to be the most dangerous threat to United's hope of winning this trophy for the first time.
The Ligue 1 side knocked out strongly fancied Roma 5-4 on aggregate in the last round and will now face Turkish team Besiktas
Elsewhere, Ajax play Schalke (who knocked out Monchengladbach) and Genk won the all-Belgian affair to set up a tie with Celta Vigo.