Bernard Trottet, 65, disappeared while walking the Cape Wrath Trail.
He was last known to be at Corryhully Bothy in Glenfinnan on Tuesday 27 May.
Police Scotland said he was planning to walk north to Kinloch Hourn and then on to a campsite in the Morvich area but failed to arrive.
The force said a body was found in the water in the Kinloch Hourn area around 12.55pm on Monday.
It said: “Formal identification has yet to take place, however, the family of Bernard Trottet, who was reported missing in the area, has been informed.”
There are not believed to be any suspicious circumstances and a report will be submitted to the Procurator Fiscal, police added.
The Cape Wrath Trail is a hiking route that runs around 200 miles through the Scottish Highlands and the west coast of Scotland.
It is considered one of the most challenging long-distance walks in the UK.
Police have been searching for Mr Trottet, with assistance from air support and mountain rescue teams.
Read more from Sky News:
Family of missing teen ‘living through hell’
Man jailed over ‘first date’ chase that ended in police car pile-up
