Harland and Wolff workers say they need an investor with a long-term commitment to Northern Ireland as the Belfast shipyard faces closure.
Workers say they are becoming "extremely concerned" over mounting speculation that Newry-based MJM Marine could be a potential bidder post-administration.
Trade union Unite, which represents some of the workers, has warned against the move saying it will be a "brand-stripper".
Workers have occupied the yard since Monday July 29, holding a 24/7 picket ahead of the arrival of administrators this Monday.
Harland and Wolff has been unable to find a buyer after being put up for sale amid serious financial problems at its Norwegian parent company.
Unite regional coordinating officer Susan Fitzgerald said: "As administrators prepare to move into Harland and Wolff tomorrow, workers are extremely concerned at speculation that the MJM group, which had been in exclusive negotiations with Harland and Wolff before abruptly pulling out two weeks ago, may to be looking to buy the yard in a post-administration situation.
"This would be a cynical move designed to jettison jobs and workers.
"We know that MJM has already outlined its plans to Invest NI and the Department for the Economy – plans in which the workers are surplus to requirements.
"There is still time for the government to put aside its ideological prejudices and re-nationalise Harland and Wolff."
Meanwhile, dozens of workers and their families attended a family day event at the protest site on Sunday.
Some of the entertainment included face painting and bouncy castles as workers were joined by their wives, partners, children and grandchildren.
Chris Neil, a security operations manager, has worked at the company for 13 years.
He attended the event with his partner Sarah Minford and their six-month-old baby, Lacie Neil.
"It's a bittersweet day. We are hoping something will happen," he said.
"We have until 5.15pm on Monday but we are still hopeful something will come through.
"Tomorrow could be our last day here. I love the place, the experiences it has given me over all this time has been incredible.
"If tomorrow is the end, I will leave with no regrets.
"There's a lot of lip service from politicians and you would think that it being such an historic company that means so much to the city of Belfast, a solution would be found."
Marcus Kane (47) has worked at the firm for almost six years.
He attended the family day event with his wife, Julie, and their eight-year-old daughter, Elise.
"It's been tough on families but it's great to see everyone pulling together in the midst of all that is happening. It's helping take our minds off things," he said.
"It's very unsettling to go out and look for work. I don't know how long it will take to find a new job.
"On the face of it politicians want to help but unfortunately Belfast City Council can only lobby on our behalf.
"I think come tomorrow it's the last-ditch attempt to get the money."
Operations manager Brian Walsh has been working for the company for seven years.
"We are really in limbo. As far as government agencies are concerned we are not getting any help, talk is very cheap," he said.
"All these men have families and they all rely on these wages.
"If this place closes that will be the end of heavy industries here.
"It's sad this won't be here for future generations."
