The levy would apply to Kiwi and overseas visitors and could raise between $20 million and $30 million a year. The charge would replace ratepayer-funded spending to attract visitors and support major events.
Key said Goff might be able to introduce a targeted rate on accommodation providers, which would not need Government support.
The tourism industry says the levy is unfair because visitors already help the Auckland economy.
Tourism Industry Aotearoa chief executive Chris Roberts said the council should support tourism growth in Auckland, not trying to fleece the golden goose.
Hospitality New Zealand has also expressed concern at the proposed levy.
Rachael Shadbolt, Hospitality NZ general manager of accommodation, said it took a too narrow view of who benefits from tourism and unfairly targeted only hotels, motels, apartments, backpackers and the like.
"We welcome the opportunity to engage with council on this. However, in its current proposed structure it is unlikely we or our commercial accommodation members in Auckland would support such a move," she said.
Shadbolt said a visitor levy had been whirling around the industry for years and Hospitality New Zealand's preference would be for a national discussion rather than individual councils setting up their own systems "which would be administratively burdensome not to mention confusing".
The city's largest hotel operator, AccorHotels, is "categorically" opposed to a visitor levy.
AccorHotels senior vice-president operations for New Zealand, Fiji & French Polynesia, Chris Sedgwick, said it was extremely disappointing that the mayor would propose a visitor bed levy that will unfairly target commercial accommodation providers and travellers who bring associated economic benefits throughout Auckland.
Sedgwick said a levy "ultimately will be absorbed by the hotel guest, in turn this means they will have less discretionary spend to enjoy Auckland's tourism attractions, dining and retail outlets".
AccorHotels operates the Sofitel Auckland Viaduct Harbour, Pullman Auckland, Mercure Auckland, The Sebel Quay West, The Sebel Auckland Viaduct Harbour, Novotel & ibis Auckland Ellerslie, Novotel & ibis Budget Auckland Airport and ibis Budget Auckland Central.
A spokesman for SkyCity, which has two hotels and is the largest ratepayer in the city, said the company did not wish to rush in and comment but was "sure we will have a view in time".