United topped the table in November but are now six points adrift of the top four with 13 matches left.
The possibility of failing to qualify for the Champions League has clearly concerned investors.
United's share price dropped from $20.47 to $19.57 on Monday morning.
That figure is the lowest price since December 2012. Not even during the darkest days of David Moyes' reign had United's shares been valued so lowly.
United's share price dropped by 2.6 per cent in morning trading on the New York Stock Exchange before rising above the $19 mark again in the afternoon.
Ed Woodward has secured a remarkable string of commercial deals, most notably the world record $1.52 billion kit deal with adidas, but United's performances on the pitch and their league position are of clear concern to those who invest in the club.
Investors will get their chance to grill the United executive vice-chairman during a conference call on Thursday, when the club's first-quarterly results of 2016 will also be announced.
Van Gaal bristled at suggestions he was about to be replaced by Jose Mourinho following the draw against Chelsea.
