Lochie Bellerby was one of two New Zealanders among the 43 people who were on cattle ship Gulf Livestock 1, which capsized during a typhoon on September 2.
The ship left New Zealand in mid-August carrying 5800 cows to Tangshan on China's eastern coast.
Three people from the ship have been found, only two of whom survived.
New Zealand First leader Winston Peters said at the weekend New Zealand would be looking into working with partners to search for the vessel's black box.
A family spokesman said they agreed with Mr Peters, who said "it is only responsible to explore what might be possible".
"While there is still the possibility of survival of the 40 crew; in the presence of a warm summer climate, four unaccounted-for life rafts, and many island shorelines in the area where the ship sank, the family agrees with Winston Peters ... our focus should therefore remain firmly on rescue," the spokesman said in a statement.
Using co-ordinates provided by the Ministry of Foreign Affairs and Trade that included the boat’s position when it signalled distress and the position of the life raft when the second person was rescued, an independent marine consultant working with the family provided information that the spokesman said could help bring Mr Bellerby and other crew members home alive.
The consultant believed a second life raft, or raft and lifeboat, could be some 65km east-northeast of Kodakara Jima Island, towards the open ocean.
"The importance here is that the survivor two and an empty lifeboat were both spotted from the shore of Kodakara Jima Island, well outside of the original Japanese coast guard search zone."
On Friday, 216 hours after the sinking and some 154 hours since the second survivor was found in apparent good health, the family believed a search and rescue window by maritime authorities still existed.
The spokesman said Prime Minister Jacinda Ardern had indicated she was doing all she could to assist.
"If this were true, this would see her Government mandating Winston Peters, as the Minister of Foreign Affairs, to work with Japanese authorities, and taking all opportunities it could to search whilst rescue was still possible."
AAP reported on Friday that the parents of Queensland man Lukas Orda, who also went missing when the ship capsized, were reassured by the Australian Government it was working closely with Japanese authorities.
Deputy Prime Minister Michael McCormack and Foreign Minister Marise Payne said Japan's coast guard had advised the Australian embassy in Tokyo and the Australian consulate-general in Osaka that wide area surveillance by air and sea continued.
"Australia is encouraging Japan's ongoing air and sea efforts, and continues to offer the Japanese authorities any supporting capability needed.
"Japan's Coast Guard has assured Australia it will not give up its search for those missing."
