Moyes saw his 10-month reign as Sir Alex Ferguson's successor brought to an end last week, with Ryan Giggs appointed as interim boss and beginning his tenure with a 4-0 thrashing of Norwich City on Saturday.
Van Gaal, though, is heavy favourite to take the Old Trafford hotseat on a permanent basis after the World Cup, when his contract with the Netherlands national team expires, with speculation going as far as claiming that the 62-year-old has already agreed to fill the vacancy in the summer.
The former Bayern Munich and Barcelona boss has stressed that these rumours are not accurate, while dismissing suggestions that his age does not make him a suitable option to help United rebuild.
"No, I didn't meet them," Van Gaal is quoted as saying by The Sun. "Am I young enough for the job? I think you can see that in my CV."
Van Gaal, who won the 1995 Champions League during his time in charge of Ajax, has admitted his desire to test himself in the Premier League and had previously been linked with Tottenham Hotspur.