The Spherical Tokamak for Energy Production (STEP) project is backed by the UK Atomic Energy Authority (UKAEA), which has said a plant would create "thousands" of jobs as well as "a near-limitless source of low carbon energy".
Moorside is near Seallafield in Copeland and was previously linked with a nuclear new build project backed by Toshiba but that plan did not go ahead following financial troubles for the Japanese firm.
A STEP reactor is designed to be compact and would be build in the shape of a sphere, inside which it would enable nuclear fusion to create energy. Most reactors use a different process, known as fission.
The UKAEA explained that fusion is the same process which powers the sun and other stars and has claimed it will create 4m times more energy for every kilogram of fuel used compared to burning coal, oil or gas.
It is hoped a prototype would help make the process a commercial viability and the UKAEA is targeting first operations in the early 2040s.
The news that Moorside has been shortlisted has been welcomed by business and political leaders in Cumbria.
The others sites being considered are Ardeer in North Ayrshire, Goole in East Yorkshire, Ratcliffe-on-Soar in Nottinghamshire and Severn Edge, which straddles South Gloucestershire and Gloucestershire. Fifteen sites were long-listed following an open call for between December last year and March.
The shorlisted places will be assessed for their suitability, with a final decision set to be made by the Secretary of State at the Department of Business, Energy and Industrial Strategy (BEIS) next year. Construction would be expected to start in 2024.
Jo Lappin, the chief executive of Cumbria Local Enterprise Partnership, said:
Paul Methven, STEP programme director at the UKAEA, added: "Through the next phase of assessment, we look forward to working with the shortlisted sites and local communities to gain a more in-depth understanding of the socio-economic, commercial and technical conditions associated with each site, before we make our final recommendations to the Secretary of State in 2022."