"Wayne's injury is more heavy than we thought and it's a nasty injury," Van Gaal told the club's website (www.manutd.com) on Friday.
"When we go on it's been getting worse. We have to let him train to make the ankle stronger, that's very important.
"I cannot say (how long he'll be out) because the doctor shall decide that with Wayne of course. He is training well in the rehabilitation."
Van Gaal also confirmed that Rojo had dislocated his shoulder in training and bemoaned his luck at the string of "unavoidable" injuries his players had suffered.
"Rojo has been injured. It's his shoulder, the same as last year, in a training session. It's very unfortunate, also in the position of Luke Shaw so I have a great problem," he said.
"I have already given the players two days off this week. I am giving them a lot of rest because I think it is necessary now, nevertheless we have six injuries most of which are contact injuries.
"You cannot avoid those because football is a sport with direct resistance. We are unlucky I have to say."
Phil Jones (ankle/foot) and Ander Herrera (hamstring) are also ruled out against eighth-placed West Ham, but young midfielder Jesse Lingard (hamstring) is returning to fitness after missing the game against Leicester.
(Reporting by Simon Jennings in Bengaluru; editing by Toby Davis)
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