Van Zweden is reported to have made the remark to Dutch TV ahead of the Swans’ 2-1 victory over United on Sunday.
In a statement issued by the club on Tuesday, chairman Huw Jenkins said he was “disappointed” a member of his board had put the club’s relationship with others in jeopardy.
He said: “It is disappointing that one of our directors has apparently made a statement in the media in relation to a manager of another football club.
“Our football club prides itself on having a good working relationship with all Premier League clubs, managers and staff. We feel we have built up that good relationship over a number of years and will continue to work hard to preserve our image.
“If any of our directors behave in an inappropriate and unprofessional manner not befitting this football club then they will be dealt with internally and appropriately.”
Van Zweden tweeted a number of times directly at van Gaal while celebrating the result, which confirmed Swansea’s Premier League double over United this season.