But Symi’s mayor, Eleftherios Papakalodoukans, said firefighters had told him it was “impossible” that Dr Mosley was still there.
“It’s a very small, controlled area and it’s full of people, so if something had happened to him there we would have found him by now,” he told the BBC.
A local journalist said there were unfounded rumours that Dr Mosley may have fallen into the sea.
George Evgenidis, an anchor for Greece’s Star TV channel, told Express.co.uk: “We were surprised when the news broke, but accidents involving tourists are not uncommon in Greece during the summer.”
“But the story took on another dimension when it emerged that the missing person was a well-known British nutritionist. I think this is why the authorities are putting so much zeal and enthusiasm into the search and rescue operation.”
“There are no official information or updates on the progress of the search, but one scenario being considered is that he fell off the rocks and into the sea, which would mean a search and rescue operation would be more complicated than if he had had an accident on land.”
“For better or worse, this incident happened on a small island and in a small space people are talking, but the scenarios being discussed among locals have little to do with the actual situation.
“For example, there are witnesses who say he was at a bus stop on the island. From what I understand, authorities are further investigating the scenario that he fell off a cliff and then into the sea.”
“The injury could have been caused by a slip, trip or fall or even a snake bite,” Greek police spokeswoman Konstantina Dimoglidou told the Daily Mail, adding that “all possibilities are on the table and investigations are ongoing.”
A Foreign Office spokesman said: “We are supporting the family of a British man who is missing in Greece and are in contact with local authorities.”