The proposed 1-billion pound (1.38-billion-euro, USD 1.47-billion) project would harness the huge tides from the Severn Estuary which separates England from Wales, with the goal of powering 155,000 homes for 120 years.
The company behind the project, Tidal Lagoon Power, says it will require subsidies of about 168 pound per megawatt hour (MWh).
This would make it significantly more expensive than other low carbon energy, although its backers hope it would be the first of five more tidal lagoons in Britain.
A Treasury spokesman told AFP that talks were due to begin within weeks "to assess whether it is an affordable opportunity, and whether the proposal is value for money".
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The project envisages building a 9.5-kilometre (six-mile) seawall fitted with 16 hydro turbines around Swansea Bay, where the waters rise and fall by up to 10.5 metres.
It still needs to win planning permission from the local authority, but if approved would be connected to the national power grid by 2019, providing 495,00 MWh every year.
"It's a game-changer. In a single step it presents the option to harness indigenous, renewable electricity at a low cost and a nuclear scale," he said.
"These projects can now be developed relatively quickly and will outlive all of us. The government recognises that we cannot afford to overlook these opportunities."
A separate project is underway in Pentland Firth off northeast Scotland to power 175,000 homes by harnessing tidal movement through underwater turbines but without the creation of an artificial seawall.