Edward Davies, 39, from Hampshire, has not been in touch with his family or friends since Sunday 8 May.
Extensive searches involving mountain rescue teams, search dogs, police and a helicopter have been made since he was reported missing the following Wednesday.
Mr Davies, an experienced hillwalker, had planned to climb Sgurr na h-Ulaidh.
In a statement released on Tuesday, his family said they still held "every hope" of him being found alive.
They have been told by police of the discovery of the body.
A body has been found during a search of Glen Coe for a hillwalker who was reported missing last week.