Shipbuilding unions are seeking a meeting with Defence Secretary Geoff Hoon in an attempt to end uncertainty over the future of Scottish yards.
Unions fear the yards may be sold
Amicus fears that Vosper Thornycroft would switch contracts to Portsmouth if it bought BAE Systems, taking work away from the yards at Govan and Scotstoun.
There could also be implications for Babcock's Rosyth yard, the union said.
It wants Mr Hoon to seek assurances that at least one of the companies has a long-term commitment to Scotland.
Amicus said it would also use a meeting to discuss whether BAE Systems was actively seeking a sale of the Clyde yards or whether approaches from Vosper Thornycroft were unsolicited.
BAE recently said it was "reviewing its options" on the business and would consider selling it.
The company holds the contract to build six Type 45 Destroyers for the Royal Navy at Govan and Scotstoun.
It also has a joint contract with Babcock at Rosyth for the CVF super aircraft carrier.
"Loss of one or other of these would result in closure of both facilities at the Firth of Forth and Clyde," said an Amicus spokesperson.
The union's regional organiser, Bernie Hamilton, said there was a south coast bias within the naval establishment.
"The continued need for campaigns to save Rosyth and now to fend off corporate asset strippers for the hard-won Clyde yard contracts demonstrate this," he said.
"We are today calling for an urgent face-to-face meeting with Geoff Hoon to secure the contracts announced for these two pillars of Scottish industry and therefore stop the possibility of any kind of asset stripping of our shipbuilding heritage."