Witnesses claim Michael Mosley spoke to a mystery person just before he disappeared in Symi, the mayor of the island has said.
The TV doctor's wife, Clare reported him missing late on Wednesday evening after he failed to return home and an urgent appeal was published on a local Facebook page.
CCTV footage appears to show the missing 67-year-old just 30 minutes after he set off for a coastal walk.
The island's mayor, Lefteris Papakalodoukas told Greek media that witnesses had seen the TV star speaking to another person after his walk.
Michael Mosley was captured on CCTV footage on the day he went missingSome witnesses reported that Mosley was seen talking to a woman after leaving the beach, according to Papakalodoukas.
However, the Greek mayor said other witnesses reported him speaking to a man in Pedi - a 15-minute walk away.
"The whole island is in turmoil. The volunteers of the island and the services are out looking to find him," he told Live News.
"The information we have says that he returned from the beach of Agios Nikolaos, walked the footpath which is 10-15 minutes and arrived at Pedi, which is a residential area."
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He added: "It is not easy for a person to go missing in Symi. I think if something had happened, since last night when they were searching and scouring Pedi, we would have found some trace.
"The beach is accessible on foot, there is no elevation. I am almost certain that nothing has happened, the man must have gone somewhere. Unless they say they saw him in Pedi, when they didn't.
"All of these are testimonies that are being investigated at the moment.
"The mobilisation of the police and the fire brigade is great and we hope that the man is found quickly and that he is in good health."
The TV doctor's wife, Clare reported him missing late on Wednesday evening after he failed to return home
Reuters
According to police the doctor set off to walk back from St Nicholas at around 1.30pm.
The latest CCTV shows Mosley at Blue Corner in Pedi at 1.52pm - which is a 15-minute walk from St Nicholas and a quarter of the way through the walk he had set out on.
Police in the area have reportedly promised "more men" will soon be enlisted to help with the search while helicopters and drones have also been deployed.
