United lost 2-1 to the Danish minnows in their Europa League last-32 first leg and need to turn the result around at Old Trafford on Thursday if they are to progress in the competition.
Another poor display at Old Trafford would pile even more pressure on Van Gaal, who "sought answers for their inept display [against Midtjylland] and the team's recent poor form" in lengthy one-on-one meetings with his squad on Friday, per Simon Jones in the Daily Mail.
Jones reported United's players "spent up to 20 minutes each" with Van Gaal as he asked them to explain what went wrong and how it could be fixed, with the Dutchman concerned about why his methods seem to be having so little impact.
The defeat to Midtjylland came on the back of a 2-1 loss to Sunderland in the Premier League, which further reduced United's chances of finishing this season in the top four—they are six points back from Manchester City in the last Champions League qualification spot with 12 games to go.
Failure to qualify for Europe's premier club competition is what eventually led to David Moyes losing the Old Trafford top job in 2014, and Van Gaal looks alarmingly close to suffering the same fate.
Reports indicate Jose Mourinho is increasingly likely to succeed Van Gaal in the summer, despite the Dutchman's United contract running until 2017, per Samuel Luckhurst in the Manchester Evening News.
Bleacher Report's Dean Jones believes the appointment of the Portuguese could help United get back on track:
Per Jones, "there is a growing belief" among the United players that Ryan Giggs could be the man to take over from Van Gaal.
The former Ajax and Barcelona boss' future at Old Trafford is uncertain to say the least, and he clearly believes his squad are failing him in some respects, hence the need for the inquest, via BBC Radio 4's Nick Sutton:
United bounced back from the Midtjylland defeat with a 3-0 win over League 1's Shrewsbury Town in the FA Cup fifth round on Monday.
However, Thursday's clash with Midtjylland and Sunday's fixture against Arsenal will be more indicative of whether Van Gaal's meetings have had the desired effect. And they could make or break United's season.
If United are knocked out of the Europa League by Midtjylland, Van Gaal could be gone before the Arsenal game. Anything other than a win at Old Trafford in that match would surely see the Red Devils' top-four hopes gone for good.
However, two victories would most certainly ease the pressure on Van Gaal—at least for now—and provide a potentially vital boost moving into the latter stages of the season.