The bar manager who was with the journalist found the body, according to the PA news agency, which reported that the island's mayor had alerted staff after “seeing something” next to the bar's fence.
Agia Marina bar manager Ilias Tsavaris said: “He called me and said, ‘We saw something in the distance. Would you like to go check it out?’ So I went there.
“So when I walked over, I saw what looked like a dead body.”
Rescue workers were searching the area daily using helicopters, he added.
A coroner is sent to Symi. Police spokeswoman Konstantia Dimoglidou told the BBC authorities had to rule out the possibility that the death was the result of criminal activity.
“We need to get the first insight into the cause of death and whether death occurred before hitting the ground,” Mr Dimoglidou said.
Greek authorities conducted an extensive search for Dr Mosley over five days in high temperatures.
The effort involved firefighters, dogs, helicopters, drones, local residents, Simi and officers from off-island.
On Saturday, BBC News obtained CCTV footage showing one of the last sightings of a man believed to be Dr Mosley walking with an umbrella next to a marina in the village of Pedi on Wednesday.
His four children were also on the island with his wife, Dr. Clare Bailey Mosley.
