Detectives are to travel to France to investigate whether the Earl of Shaftesbury has been murdered.
The Earl has not contacted family or friends since 5 November
The 66-year-old aristocrat, who has homes in London, Hove, and the French Riviera, vanished on a trip to France.
He was due to return to the UK on 10 November but has not been seen since checking into a hotel four days before.
Sussex Police officers are to liaise with their French counterparts in Nice. Police said they were looking at the possibility the earl had been murdered.
'Out of character'
"This remains a French-led investigation and the possibility that the Earl of Shaftesbury has been murdered cannot be ruled out.
"We will assist the French authorities in anyway we can with specific lines of inquiry when required," said Detective Chief Superintendent Graham Cox, from Sussex Police.
The three-times-married earl, whose name is Anthony Ashley-Cooper and whose family seat is at Wimborne, Dorset, arrived in Nice on 3 November.
He contacted his family on 5 November but they have not heard from him since.
Detective Chief Inspector Adam Hibbert said: "This is completely out of character and very worrying for his family and friends."
Police described the earl as being of thin build with thinning grey hair.
They said he often wears large, heavy-framed red and pink glasses and normally wears a large watch and casual clothes.
The Sussex officers are due to travel to France on 13 December for a week.