Meanwhile, courtesy of a comeback win over Istanbul Basaksehir, their Danish opponents have reached this stage of the competition for the first time in their history.
After a gruelling end to their domestic schedule, United boss Ole Gunnar Solskjaer jumped at the opportunity to rest his star men for the second leg of their last-16 tie with LASK Linz.
As well as handing much-needed minutes to his backup players, their performance would have strengthened Solskjaer's feeling that a gap has emerged between the first XI and the rest of his squad.
While a below-par showing was mainly down to a lack of match sharpness, none of the nine outfield players which came into the team staked their claim for a role on Monday evening.
Nevertheless, less uncertainty over his selections may suit Solskjaer at this stage of the season as United bid to live up to their tag of competition favourites.
Although the draw has no doubt been kind to the Premier League giants, they will have to be wary of Copenhagen relishing the opportunity of playing without any pressure on their shoulders.
Stale Solbakken has worked wonders to get the club to this stage of the competition, only suffering two defeats in 10 matches since the beginning of the group stages.
Like with their next opponents, the draw has been kind, but Copenhagen were underdogs heading into their knockout ties against Celtic and Istanbul Basaksehir.
Their most recent success, by a 3-0 margin on Wednesday, came after losing the first leg in Turkey, and it represented the second tie in succession where they have recovered from poor results in the opening fixture.
That said, facing United in a one-off contest in Cologne will suit this team as former Wolverhampton Wanderers boss Solbakken looks to remind people in England of his coaching credentials after his disastrous spell at Molineux.
Manchester United Europa League form: LWDWWW
Manchester United form (all competitions): DWLDWW
Copenhagen Europa League form: WLDWLW
Copenhagen form (all competitions): LDLWWW
Solbakken is expected to make minimal changes to his first XI after their impressive showing on Wednesday.
Guillermo Varela, who played 11 times for United during the 2015-16 campaign, will line up at right-back.
Jonas Wind is regarded as one of Copenhagen's danger men after scoring twice and providing an assist against Basaksehir.
Manchester United possible starting lineup:
De Gea; Wan-Bissaka, Lindelof, Maguire, Williams; Pogba, Matic; Greenwood, Fernandes, Rashford; Martial
Copenhagen possible starting lineup:
Johnsson; Varela, Nelsson, Bjelland, Boilesen; Mudrazija, Zeca; Biel, Wind, Jensen; Kaufmann
We say: Manchester United 4-1 Copenhagen
Being heavy underdogs in this tie could suit Copenhagen, who may be prepared to sit deep during the early stages in a bid to frustrate their opponents. However, United's superior quality should shine through at some stage, keeping them on course for the final.