BAE UK chief executive Nigel Whitehead is reported as saying that the arms company might "reduce its footprint" after the completion of the two Queen Elizabeth class aircraft carriers.
He said: "Part of that might actually be the cessation of manufacturing at one of the sites."
BAE, which operates in UK locations from Glasgow and Scotstoun to Portsmouth, reported a 14% fall in sales in 2011 as military spending in the US and UK was cut.
An industry insider reported that the Portsmouth base was believed to be most at risk because of its high numbers of temporary staff. However, Mr Whitehead said the decision on closures had not yet been taken.
"We will be making decisions this year, so we have a number of weeks in which to do that," he said.
Ian Waddell, national officer for shipbuilding at the Unite union, said: "From our point of view we’d rather just have a decision and get on with it."
"There’s clearly a workload gap and even then it’s not clear if there’s enough work to sustain the three yards. A merger, with a jobs guarantee, would have created a strong new company that could have protected the UK's long-term interests."
The statements come after a proposed merger between two giant arms firms had been shot down after German opposition forced bosses to ditch the bid.
The proposed merger of BAE Systems and EADS would have created a company with combined sales of £60bn and more than 220,000 staff, with around 52,000 British workers alone.
But after days of political wrangling, the two companies were forced to ditch the bid, giving rise to fears over job security at BAE's facilities, which include the Govan and Scotstoun shipyards in Glasgow.
Unions, defence analysts and politicians all raised concerns, saying that the merger would have created a stronger company and guaranteed jobs in the long term.
David Reeths, director of consulting at defence analyst IHS Jane's, said: "This will mean that job guarantees that would have been part of the deal will not be made.
"While the UK Government was seen to have supported the merger, the Government may face demands for more direct industry support to secure BAE's future."
The Unite union urged the UK Government to strengthen its "golden share" in BAE by taking an active stake in the company to safeguard British jobs and boost manufacturing.
Unite, which represents more than 30,000 skilled British workers across the two companies, had been pressing for guarantees over jobs if the merger had gone ahead.
Mike Clancy, general secretary designate of Prospect, representing engineers and specialists working for BAE, said: "This decision changes nothing immediately, but it raises profound questions for the future of the defence sector and the UK's industrial base, which has been shown by this merger to be in crisis.
"Thousands of skilled jobs have been lost at BAE over the last two years and we fear the loss of thousands more if BAE cannot expand its order book into new markets.
"BAE is a prime contractor for the Ministry of Defence and this move clearly reflects fears about the future profitability of those arrangements as defence markets shrink."
It is also believed that the USA had concerns over sensitive military assets transferring from British ownership to a European business.
Report from Ian Bell