(CNN) -- Two men found floating in a giant cooler off the Australian coast say they want to stay in Australia and don't want to go home, immigration officials said Friday.
The Australian Customs Service found the two men in the Torres Strait on January 17.
The men will be transferred to Christmas Island in the Indian Ocean, where Australia has an immigration detention facility, a spokesman for the Department of Immigration and Citizenship told CNN.
"The men have both indicated they do not wish to return to their home country," said the spokesman, who asked not to be named. "They will remain in detention on Christmas Island while immigration officials consider any claims to remain in Australia."
The spokesman declined to reveal the men's nationality or what claims they have made to remain. Australian media reports have said the men are from Myanmar.
The Australian Customs Service spotted the two men January 17 floating in a giant red icebox, or cooler, in the Torres Strait, between the northeastern tip of Australia and Papua New Guinea, a Customs spokesman said. Customs agents had been on a routine mission to identify possible smugglers in the area at the time, the spokesman said.
A picture taken by Australian Customs shows the men standing in the floating cooler and waving at authorities. The sides of the box are waist-high.
After their rescue by helicopter, the two men spent several days in a hospital, an immigration spokesman said. They were then housed in detention while officials interviewed and processed them, the spokesman said.
Australian media reports said the men spent 25 days afloat in the cooler, surviving only by drinking rainwater and eating regurgitated fish dropped by birds.
Lee Hollingsworth of the Royal Society for the Protection of Birds told CNN it was not uncommon for Asian fishermen to use birds such as cormorants to dive down and retrieve fish that are then regurgitated whole.