Van Gaal is currently manager of the Netherlands national team but will be leaving his post after the World Cup.
According to The Mirror, United have held preliminary talks with the former Barcelona boss as pressure grows on Moyes.
Tottenham Hotspur have reportedly been talking to Van Gaal for a while now, and the Dutchman's stalling could be down to developments with United.
United have endured a disappointing season under Moyes and are currently seventh in the Premier League with five games to go.
Van Gaal has had success at Ajax as well as Barca in the past, and it is thought that his relationship with Robin van Persie could also aid his chances of replacing Moyes.