The coastguard received a distress alert at about 3.45am on Saturday, and the boat’s emergency positioning beacon was activated near the island of Mingulay.
A search operation for the missing sailor has been scaled back.
Mark Rodaway, a national maritime operations commander with the UK Coastguard, said: “Despite an intensive search including the helicopters, lifeboat and other fishing vessels in the area, we have been unable to locate the missing fisherman. Our thoughts are with all those involved.”
It is believed that weather conditions were relatively calm when the vessel went down.
A Maritime and Coastguard Agency spokeswoman added: “The coastguard search and rescue helicopter based at Stornoway has been searching the area along with the Barra RNLI lifeboat.
“The lifeboat remains in the area and the coastguard search and rescue helicopter from Prestwick has taken over so the search can continue.”