BAE Systems, which owns the Govan and Scotstoun yards, is discussing plans to merge with Airbus aircraft manufacturer European Aeronautic, Defence and Space (EADS).
The defence company, which employs around 3000 shipyard workers in the West and Southside of the city, would form the world's biggest aerospace and defence company if the tie-in goes ahead.
The merged group would employ around 220,000 staff, including 48,000 in the UK, with combined sales of some £60billion.
As reported in the Evening Times earlier this month, the last Type 45 warship to be built on the Clyde – HMS Duncan – slipped out of Scotstoun shipyard on Friday, August 31.
The battleship, which is one of the world's most advanced, was the last in a £6bn fleet to be built in the city.
The ship sailed off for three weeks of manoeuvres off the west coast of Scotland during which engineers were set to test the destroyer's power and propulsion systems.
The warship will be handed over to the Royal Navy next year, as was sister ship HMS Defender earlier in the summer.
A BAE spokeswoman said it was too early to confirm whether there would be any job losses linked to the merger, but stressed there was very little overlap between the two business activities.
Keith Hazlewood, national officer of the GMB union said: "This is a worrying development as so much of our high-end engineering and manufacturing skills are embodied in this company.
"The UK Government must play a proactive role as this company contains the skills vital to the defence of our nation."
EADS, a consortium of aerospace and defence manufacturers from France, Germany and Spain headquartered in Paris and Berlin, has the majority of its work in the commercial sector while BAE is an expert in the field of defence, security and military.
BAE said: "BAE Systems and EADS have a long history of collaboration and are currently partners in a number of important projects, including the Eurofighter."
Shares in the London-based BAE soared 11% on the news of the talks. BAE said the proposed deal would be a merger, but would see BAE shareholders own 40% of the combined group and EADS shareholders own 60%.
BAE produces Astute nuclear-powered submarines and is the largest supplier of land vehicles to the US army.
But BAE has been under pressure, reporting a 14% fall in sales last year. This saw 2011 profits fall 7% to £2bn.