The defence giant insists it has made no final decision on the future of its two Clyde yards.
However, the company yesterday began to brief workers on two options for its warship business: building across both sites or focusing all its investment and resources on Scotstoun.
BAE Systems has also begun informal talks with planning officials at Glasgow City Council over expanding the yard on the north bank of the Clyde.
Last month the company announced more than 1700 job losses over the next three years as it winds down from its current orders building two giant aircraft carriers.
Some 800 of those posts will go in Scotland with most of the rest in Portsmouth, where its yard will go back to its previous work repairing rather than building ships.
It is understood that BAE Systems will need the same number of workers whether it operates over two yards in Glasgow or one.
There was substantial speculation before the announ-cement last month that Govan, as well as Portsmouth, would close as a manufacturing base.
In fact, some industry insiders hoped this would the case. The long-term future of Scottish military shipbuilding, they feel, would be more secure with a single "state-of-the-art facility" paid for with hundreds of millions of pounds of investment and the Govan yard freed for some other purpose.
A BAE spokeswoman said: "Further to our proposal to consolidate our complex warship manufacturing capability in Glasgow, we are undertaking initial exploratory work to assess potential options to invest in these manufacturing facilities.
"No decisions have been made and discussions around future investment proposals are part of our ongoing consultation process with our employees and trade unions.
"Our aim is to create a world-class warship design, build and integration capability, ensuring that we deliver value for money to the Ministry of Defence and that we provide a modern, safe and inspiring workplace for our employees."
Insiders say keeping both yards open is the "baseline" option. This, sources say, would involve less investment but higher costs.
Closing Govan, which is owned by infrastructure giant Clydeport rather than BAE, would be the "enhanced" option because this would entail huge investment at Scotstoun and future-proof shipbuilding on the Clyde.
BAE is currently negotiating with the UK Government to build a new generation of frigates, called global combat ships or Type 26s, for the Royal Navy. It is expected to put detailed proposals for this work, including exactly where they will be built, to the Ministry of Defence next year.
It is currently completing work on carriers, some of it at a docks owned by Babcock in Rosyth in Fife, and preparing to build smaller patrol vessels.
The Govan yard, even if a decision was made to close it, would stay open until at least 2017 doing this work.
Some politicians in England have warned that the frigate contracts should not go to Scotland - because the country could be independent by the time the ships are made. Although the MoD routinely buys weaponry abroad it has never bought complex ships from a "foreign" shipyard.
Industry insiders, however, believe transferring the necessary skills and capacity to England from the Clyde after independence would be impractical. "It would be like Stalin moving his industry east of the Urals during the Second World War as Hitler attacked," said one.
Sources believe a world-class single facility in Scotland, should it get the go-ahead later next year, would secure long-term military shipbuilding in Glasgow after the frigates contract is completed.
No formal planning application for Scotstoun has been made. Even if it is, such a move would not commit BAE Systems to invest in the site - or shut Govan.