Aberthaw Power Station, near Barry, was the last coal-fired plant in Wales.
The UK government has set aside £222m to produce a design concept once a site has been identified.
Communities had until the end of March to nominate locations.
The council hopes it could bring jobs to the region and play a role in cutting emissions.
However, the plant would not open until 2040.
What is Fusion?
Fusion – the process going on inside the sun – creates energy by forcing atoms together.
It is the opposite of standard nuclear reactors which rely on fission, breaking atoms apart.
Potentially, it can generate low-carbon power and comes without the danger of explosions.
Critics have said there are still huge hurdles to overcome and some experts believe existing, proven renewable technologies offer a more economical and timely way of tackling climate change.