The Niue government says it wants to find out if an attempt is being made to buy the flagship Matavai Resort.
The Matavai provides half of the island's tourist accommodation and is 51 percent owned by the government.
There are claims that some followers of the so-called Vastu Shastra want to buy it and allow only its members to stay.
The acting premier, Fisa Pihigia, says he will consider revoking their visas if they do not provide information about who they are and what their agenda is.
"I have directed the secretary to the government to go back to these people and demand some information from them. Because I am getting very concerned about this. If they fail to do that, then I will consider revoking their permit to stay here on Niue."
Mr Pihingia says they have temporary visas and have been staying at the resort for five months after booking five rooms until next year.