Tests are being carried out to discover whether human remains found in Russia are those of missing sailors from a trawler which sank in 1974.
The Hull-based Gaul went down in the Barents Sea off Norway with the loss of 36 men and the reason for its demise has been the subject of speculation, although an official inquiry in 2004 ruled out Cold War conspiracy theories.
Humberside Police said investigations are being carried out to determine whether the remains discovered on Russia's Rybachy peninsular in 1974 or 1975 were connected to the Gaul.
Specially trained officers have visited the families of those involved and they have been given the details known about the remains and the ongoing forensic and genetic examinations.
Assistant Chief Constable Alan Leaver said: "We have met with all the families of the crew members lost on the Gaul and will continue to provide them with information as it becomes available.
"At the moment the information we have is very limited and we have to wait for the Russian authorities to advise us of the tests they are doing on the remains. We will continue to work with the Foreign and Commonwealth Office (FCO) to seek to support families and to provide more details about the remains."
A FCO spokesman said: "We are aware of reports that a number of human remains have been found on the Rybachy peninsular in northern Russia. There is no indication yet that these are British.
"It is for the Russian authorities to determine the nationality of the remains. We have offered to provide assistance if requested.
"We are liaising closely with Humberside Police who have deployed family liaison officers to the families affected."
In 1974 the Barents Sea was a highly sensitive military area and rumours were rife that trawlers operating in the area were involved in spying.
But in 2004 then attorney general Lord Goldsmith told the inquiry: ' 'There is nothing which suggests that the Gaul was engaged in any activity other than fishing on her last voyage and there is nothing to suggest that anyone on board her was engaged in any activity other than fishing on that voyage.''
The public inquiry concluded the Gaul went down in heavy storms and was not deliberately sunk by the Soviet Union or pulled down by a submarine.
The remains of James Wales, Maurice Spurgeon, Stanley Collier and Clifford Briggs were found in 2002 but those of the rest of the crew have not been discovered.
Beryl Betts, whose brother Billy Jones was a 26-year-old deckhand on the Gaul, said she had "mixed feelings" about the latest development.
She said police had told her between five and 10 sets of remains were being investigated and blamed the Cold War tension between Russia and the UK for the delay in making progress since their discovery in the mid-1970s.
Mrs Betts, 74, from Hull, said she would have preferred for officials to have waited until there was certainty over whether the bodies were from the Gaul before the families were approached.
"I have mixed feelings about it. My personal opinion is that they should have told us when they were 100% sure. This has spoilt Christmas," she said.
The thought that the bodies could be identified was "at the back of your mind all the time", she said.
Mrs Betts, who is giving a new DNA sample to police to potentially aid in the identification process, said she had spoken to some of the other relatives of the Gaul's crew.
"They are all in a state of shock, I was very shocked," she said.
"Will we get any further answers? Because the inquiry was a whitewash."
She said it was now up to the Russians to provide answers, but she had been given no indication of how long the process would take.
Mrs Betts said: "They have no idea. It is 'how long is a piece of string?', we could have this hanging over our heads for another year."
She added: "There's still a lot more questions than answers."