The trade body is lobbying the Ministry of Finance to abolish consumers' right to pay in cash at all shops and restaurants.
"Tourism is well-suited for a trial of such a new practice," the NHA's managing director Jostein Hansen argued, explaining that making all restaurants and hotels cash-free would prevent "disreputable" hoteliers and restauranteurs from avoiding tax.
The Finance Ministry has so far resisted the proposal. "Being able to pay cash is a privilege we want to keep," state secretary Morten Søberg told the newspaper.
The NHA expects that a new conservative government, if elected in September, will look more favourably on the idea.