The Liverpool boss was beaten 3-1 by the former Barcelona and Bayern Munich coach in the final of the International Champions Cup and responded by suggesting that his 62-year-old counterpart would face far sterner tests when the Premier League kicks off.
But Giggs, now assistant manager at Old Trafford, believes that Van Gaal will adapt seamlessly to life with the 20-time English champions and is confident that he is ready for the challenge.
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"Even the manager has realised how big this club is in the short space of time he has been here. The crowds for friendlies are 'unbelievable' in his words.
"He's managed at the top level for a long, long time and won't be intimidated or afraid of managing Manchester United."
Giggs says that the players have responded well to Van Gaal’s arrival, despite prior reports that the Dutchman is a strict disciplinarian, and hailed his meticulous attention to detail.
"I think he's a great character. He is, first and foremost, a leader and demands respect, demands discipline and a real sort of detailed structure," Giggs continued.
"But, within that structure, there is obviously freedom to move. It's been great. The players have really enjoyed it so far and I certainly have.
"Everything is structured and really detailed. I think the lads have all enjoyed all the things that have come that are a little bit different. Right down to meeting for breakfast, and for lunch, and even the team meetings that we have. Plus the training."