Mark Clarke went fishing early Monday and his unmanned 25-foot (7.6-metre) sailboat was found lodged on a northern reef off the island of Grand Cayman the next day, the Royal Cayman Islands Police Service said.
He sailed for the Caribbean territory at the Olympic Games in Barcelona, Spain, in 1992 and the US city of Atlanta in 1996.
Marine Commander Ian Yearwood said authorities were still looking for the 63-year-old sailor but they had told his family they believed it "extremely unlikely that he would be found alive."
"Despite a widespread air, land and sea search, no trace of Mr Clarke has been found," said Yearwood, who was once a colleague of the missing man when he was employed with the three-island territory's police force.
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Donald McLean, president of the Cayman Islands Olympic Committee and one of Clarke's Olympic teammates, said the weather and marine conditions were good when he disappeared.
"Everyone's been very much in a state of shock since his disappearance. He is a very passionate, extremely competent sailor," McLean said in phone interview.
The Cayman Islands are about 150 miles (240 kilometers) south of Cuba.