John van Zweden is alleged to have made the comments on Dutch television on Saturday - the same day as Swansea's 2-1 win over United in the Premier League.
With chairman Huw Jenkins stating this week the club would look into the matter, Monk told a news conference on Thursday he did not find Van Gaal to be arrogant.
"I was made aware of [the quotes], I'm not fully aware of what context it was said in or if, or what, was said but they're obviously not the views shared by myself or the club," he explained.
"I think the chairman has already said that and those sort of matters are for the chairman to deal with.
"I have no problem whatsoever [with Van Gaal], he's the character he is and he's a very experienced man - he has great belief in what he does and what people say after games can always be different to what someone else thinks.
"I didn't necessarily agree agree with the way he assessed the game at the end but it's not something that bothers me or will concern me.
"We did our job and we move on to this weekend."
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