Donald Mackenzie, 47, from Stornoway, was reported missing by a friend on 14 October after he failed to return from an expedition on Mount Ararat in Turkey.
Mr Mackenzie travels to the mountain every year to pursue his passion of searching for the ark.
His brother Ross, 49, who stays in Luxembourg, said he last had a text message from Donald on 25 September, when he was 12,000ft up the mountain.
He said: "He is very much a maverick, very self reliant, and if he went up by himself, that is a very dangerous thing to do. The most obvious scenario is he got into trouble and hurt himself, but another scenario is that in that area you get bandits.
"I've already come to terms with the fact that I probably won't see him again."
Mount Ararat is the highest peak in Turkey, at 16,945ft above sea level.
The Bible identifies the mountain range as the ark's resting place after the flood.
Mr Mackenzie's family said he had been keen to return to Turkey this year after a group of Chinese and Turkish evangelical Christians claimed to have found the remains of the ark some 13,000ft above sea level on Mount Ararat.
His mother, the renowned Gaelic singer Maggie Jean Mackenzie, said: "He was just 50 metres from it when he was there before and he just wanted to go back. He was just determined.
"Nobody wanted him to go, but he wanted to go and you couldn't keep him back. He is an adventurer and very resourceful and intrepid."