The Red Devils currently sit in fifth place following their draw with Tottenham Hotspur on Friday night, two points clear of Wednesday's opponents following the Blades' surprise 3-0 loss against Newcastle United.
With eight games of the season remaining, Manchester United find themselves in limbo to a certain extent.
As things stand, fifth place will be good enough for Champions League football next season due to Manchester City's European ban, but that has been appealed and should that appeal be successful then Man United will be consigned to another season in the Europa League.
The only way to guarantee that their European fate will not essentially be in the hands of the appeal committee is to finish in the top four, but the weekend results have harmed their chances of doing that.
A 1-1 draw with Tottenham Hotspur on Friday night would have provoked mixed emotions for Ole Gunnar Solskjaer - frustration at seeing another David de Gea mistake cost his side, disappointment at two more points dropped but also acknowledgment that Spurs are a good team and excitement at the first glimpse of Paul Pogba and Bruno Fernandes together, the latter scoring the equaliser from a penalty the former won.
However, Chelsea's come-from-behind win over Aston Villa on Sunday leaves the Red Devils five points adrift of the top four now, which is a significant deficit to make up over the closing stages of the campaign for a team that has only won 12 of their 30 top-flight outings so far in 2019-20.
Consistency has been a buzzword in the top-four race so far and Man United have certainly improved in that respect - they are now unbeaten in 12 games across all competitions - but they have also only won three of their last eight Premier League outings.
A return to their home comforts will be welcome as they play at Old Trafford for the first time since beating Manchester City in the derby on March 8, particularly having only lost once in front of their own fans since August.
Of course, those fans will not be in place this time around, which may give Sheffield United a bit more hope, although the empty stadium did not seem to provide a boost during Sunday's defeat to Newcastle.
A 3-0 Magpies win in that match was one of the last results most would have expected considering how poor Newcastle had been in front of goal, how good Sheffield United had been defensively and how difficult the Blades had been to beat this season.
The fact that all of the goals came after John Egan's red card offers a glimpse to the main reason behind the result, but Chris Wilder will be demanding a reaction from his side following their heaviest defeat of the campaign.
It has not been a particularly happy return to action for Sheffield United so far, being denied by a ghost goal against Aston Villa and then collapsing against Newcastle to make it just one point from two games since lockdown.
A top-five finish - and therefore potential Champions League football - was in their hands heading into that game against Villa, but now they need to win at Old Trafford and for Wolverhampton Wanderers to drop points in order to wrestle that control back.
The Blades have only lost back-to-back league matches once this term - away to Manchester City and Liverpool either side of the New Year - and would leapfrog Man United in the table with a win on Wednesday night.
It is therefore important to acknowledge that, regardless of what happens over the closing stages of the season, Wilder's side have enjoyed a memorable and odds-defying campaign.
However, they have won just one of their last six Premier League away games and, considering they will also be missing at least two key players against Man United, their hopes of avoiding what could be a hugely damaging result for their European chances look a lot bleaker than they did before lockdown.
Man Utd Premier League form: DWWDWD
Man Utd form (all competitions): WDWWWD
Sheffield United Premier League form: WWDWDL
Sheffield United form (all competitions): WDWWDL
Manchester United fans may finally be able to see Fernandes and Pogba play together from the start in this match, with the Frenchman's effective cameo off the bench against Spurs expected to have earned him a starting role on Wednesday.
Victor Lindelof limped off against Spurs and will be assessed in the buildup to this match, but if he is deemed fit to start then Solskjaer could name an unchanged team with the exception of Pogba.
David de Gea remains the club's number one goalkeeper for now, although his mistake against Spurs shone the spotlight on that debate once again with Dean Henderson - on loan at Sheffield United - enjoying such a good campaign.
Henderson is ineligible to face his parent club in this match, though, while the visitors will also be without the suspended John Egan following his red card on Sunday.
Wilder will therefore be hoping that Jack O'Connell is ready to return from the knee injury which has kept him out of both post-lockdown matches so far, while David McGoldrick is also pushing for inclusion.
Man Utd possible starting lineup:
De Gea; Wan-Bissaka, Lindelof, Maguire, Shaw; Pogba, Fred; James, Fernandes, Rashford; Rashford
Sheffield United possible starting lineup:
Moore; Basham, O'Connell, Robinson; Baldock, Berge, Norwood, Lundstram, Stevens; McBurnie, Sharp
We say: Man Utd 2-0 Sheffield United
Sunday's defeat to Newcastle was an anomaly for Sheffield United, but this always looked likely to be a difficult fixture for them regardless of what happened at St James' Park.
With the visitors' defensive absentees and Man United close to full strength, we are backing Solskjaer's side to pull off a crucial victory for their European hopes.