The BBC understands that 75 jobs are under threat at the Titanic Belfast visitor centre.
The company has started a consultation over the potential redundancies.
It is understood a further 11 positions are under threat at TBL International, an events company linked to Titanic Belfast and the SS Nomadic.
In a staff email, the Chief Executive of Titanic Belfast said income streams had “dried up overnight” because of Covid-19 and the closure of the venues.
Judith Owens said it had used company reserves and maximized government support packages to cover liabilities, but this was “not a sustainable situation”.
Ms Owens said a lot of hard work had been involved in building the success of Titanic Belfast “and to see its future stripped away by something beyond our control is very hard to witness”.
With projected visitor numbers estimated to be reduced by 30% and the international market not expected to return for some time, Titanic Belfast has now undertaken a strategic review of its business.
Ms Owens said part of the consultation process would consider voluntary redundancy, career breaks, part-time positions and job shares.
Titanic Belfast is due to reopen on 1 August.
In a statement to BBC News NI, the company said: “Titanic Belfast Ltd, the operator of Titanic Belfast, has notified the Department for the Economy and its staff that it is beginning a period of consultation in relation to its staffing structure to secure the future of its business.
“This is an unavoidable situation given the challenging trading environment it is now operating in, due to the devastating impact of the COVID-19 outbreak on the global tourism industry.
“Titanic Belfast recognises that this is a very challenging time for its staff, as well as its business, and therefore will not comment further on this matter.”