Van Zweden is reported to have labelled Van Gaal an "arrogant b*****d" on Dutch television on Saturday, when Swansea defeated United 2-1 in the Premier League.
Jenkins has since expressed his disappointment at the incident and says Van Zweden will be dealt with internally.
"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," Jenkins is quoted as saying.
"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 within the Premier League and the game in general at all costs.
"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."
Dutchman Van Zweden has been on the Swansea board since 2002, having initially become involved with the club as a teenager when he published a request for a pen pal in the matchday programme.
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