The Harland Shipyard and Wolff in Belfast can survive only by the end of the month without agreement, they said in the Union.
He was selling for sale due to serious financial problems in the Norwegian parent company.
Unions hope that the shipyard could use plans to build more Royal Navy vessels in the UK.
But now there is a fear that there is a risk that it will not survive long enough to participate in it.
Susan Fitzgerald, regional unions union coordinator, told the BBC News NI's Extra Evening Program if the government had to go in the yard.
The yard employs about 130 people and specializes in wind power and shipbuilding projects.
It is also part of two consortia that compete for the operation of the new cruise ship type 31e of the Navy.
The unions also point to comments by Defense Minister Penny Mordaunta who suggested that more ships be built in the UK.
Mrs Fitzgerald said the upcoming Prime Minister should follow this commitment to shipbuilding.
"We call on the government to take over the shipbuilding helm in Belfast, nationalize the shipyard, and devise a complete strategic capacity-building strategy.
"The government must not be lost to Scotland – aware of the strategic and economic importance of shipbuilding – to draft nationalization plans for Ferguson Shipyard at Clyde to secure its future."
"The best result for all stakeholders"
GMB organizer Michael Mulholland added: "The strategic and economic significance of a powerful indigenous shipbuilding sector can not be overestimated. "
It is understandable that Harland and Wolff intensively talked to one potential buyer.
The company announced that it hopes to complete the sales process at this stage, but that it is "still in negotiations with a number of potential bidders".
He added that he was trying to reach an agreement that "achieves the best outcome for all stakeholders".
Senior politicians and Invest NI have held a series of meetings with Harland and Wolff's management over the past few days.
It is one of the most famous companies in Northern Ireland and two big cranes dominate east of Belfast.
It was founded in 1861, and at the peak of production during the Second World War there were about 35,000 people employed.
His most famous vessel was the Titanic which was built in the yard between 1909 and 1911.
This was the last time the ship was built, Anvil Point, in 2003.