Jersey Museum is to close temporarily for the first time in its history to save money.
Senator Alan Maclean, who overseas tourism in Jersey, said there was plenty to do in the island despite the winter closure of the museum.
He has suggested that a yearly lottery could set up to raise money for Jersey Heritage which runs the museum.
The attraction, which features artwork as well as historical artefacts from the island, will reopen in April.
Senator Maclean said tourists have other options on the island including spa breaks.
"Food, fine dining, we have a range of wonderful restaurants of different types that attract people to the island," he said.
Robert Mackenzie, managing director of CI Travel Group, said not everybody could book a spa break.
"I think it is important to remember that only about 20% to 30% of the hotel beds in the island provide spa facilities.
"There are large number of hotels that aren't able to provide that product."
He said that some of the big events organised by Jersey tourism are working to attract people.
"The Fete de Noue has been a fantastic event, it has only been going three or four years, and has started to become an attraction people are coming here for."