Michael Mosley's four children have flown out to the Greek island of Symi to help with the search for the TV doctor, 67.
It is understood his three sons, Alexander, Jack and Daniel, as well as his daughter Katherine, are hoping to retrace his last known steps after their mother Clare reported him missing when he failed to return from a hike on the island on Wednesday.
Mosley disappeared during a walk on St Nicholas Beach in Pedi, with divers and specialist police dog units scouring the small island to search for him.
According to The Telegraph, his children have now flown out to be with their mother and assist with the search.
Local journalist Niki Kitsantonis also referenced the possibility of the sea theory while on ITV's GMB telling the hosts: "There are fears he might have slipped... The mayor of the island is worried he has perhaps (been) swept away at sea."
Mayor Eleftherios Papakalodoukas told the BBC that firefighters carrying out the search had informed him that they believed that it was "impossible" for Mosley to be in the same area he was reported missing.
Papakalodoukas added: "It is a very small, controlled area, full of people. So if something happened to him there, we would have found him by now."
Television presenters such as long-term friends Jeremy Vine and Jeremy Clarkson added to the appeals regarding information about Mosley's whereabouts, while the island's mayor has stated theories are being examined.
A new theory put forward could make the search "more complex" as police continue to comb the area where the father-of-four went missing.
Speaking to the Express, a local expert George Evgenidis has put forward a possible explanation as to why the doctor has not yet been found.
The Greek TV news anchor told the publication: "There is no official information or update on the course of the search.
"However, according to information a scenario that is being examined is that he fell off a rock and then into the sea.
"This means that the search and rescue operations will be more complex than if he had an accident on the ground."
Meanwhile, CCTV images were recently shared of Mosley just half an hour before he disappeared.
LATEST DEVELOPMENTS:
Still pictures show the father-of-four wearing a shirt and a cap, holding an umbrella.
The MailOnline reports timestamps of the CCTV as 1.52pm and taken from Blue Corner in Pedi, a 15-minute walk from St Nicholas, and a quarter of the way through the walk he had set out on.
