The Harland and Wolff shipyard in Belfast is expected to be placed into administration later.
It puts 130 jobs at risk and could spell the end of the iconic business.
Its best known vessel is the Titanic, which was built at the yard between 1909 and 1911. At its height, Harland and Wolff employed more than 30,000 people.
“It seems increasingly unlikely that a solution will be found in the short term and the company may indeed have to go into administration,” DUP MP Gavin Robinson told the BBC’s Good Morning Ulster programme.
“We’ve pulled all the political levers that we can.”
Unions want the shipyard to be nationalised, a call that has been backed by the Labour Party, but the government has said the crisis is “ultimately a commercial issue”.
Mr Robinson said Harland and Wolff had asked the government for shortfall funding of £650,000, which would have given the company “breathing space” for the month of August “so that they could explore other options”.
He added: “The official advice is that it cannot be done for three reasons: there is no order book at present so the money would be going in with no generation of product or profit; and there was no ability to secure the loans or pay them back; and it would also conflict with state aid rules.”
Last Monday, workers said they had taken control of the site and established a rota to ensure their protest continued around the clock.
Owen Reidy, assistant general secretary of the Irish Congress of Trade Unions, said “the yard should be returned to the people”.
“The entire trade union movement across these islands stands as one with the workers at the shipyard,” he said.
The shipyard was founded in 1861 by Yorkshireman Edward Harland and a German, Gustav Wolff.
By the early 20th Century, it was the world’s most prolific builder of ocean liners.
It was one of Northern Ireland’s key industrial assets during World War Two, producing 140 warships, 123 merchant ships and more than 500 tanks.
Its workforce reached a peak in the post-war years when it employed about 35,000 people.
By the late 1950s, the yard was facing increased global competition and the impact of the rise of air travel.
The launch of the Canberra in 1960 marked the last cruise liner to be built in Belfast.
By the mid-1960s the business was in serious decline.
At one stage in 1966, the management went to the old Stormont government and pleaded for a subsidy because it did not have enough money to cover the next pay day.
That was the start of more than 30 years of subsidies, during which about £1bn of taxpayers’ money was pumped into Harland and Wolff to keep it afloat.
The firm was nationalised in 1975 with the Northern Ireland Office minister, Stan Orme, describing the business as having “a sorry financial record”.
By that stage it was still employing about 10,000 people.
It returned to private ownership in 1989 through a management-employee buyout, backed by the Norwegian industrialist Fred Olsen.
It increasingly focused on the oil and gas sectors, but struggled to compete against major shipbuilders in east Asia.
The yard built its last ship in 2003 – a Ministry of Defence ferry called the Anvil Point.
Since then, it has worked on other areas of marine engineering such as oil rig refurbishment and offshore wind turbines.