The firm has had government cash to develop the power plants and hopes are high they could provide work in Lancashire for the Springfields nuclear fuel plant at Salwick, safeguarding many of the 1,000 jobs there.
Rolls Royce is looking for a manufacturing site for the pre-fabricated parts for the new reactors, which are smaller and cheaper than the previous generation of power plants, and these parts will be assembled on the site of the power stations when identified.
It is thought the sites for the new 470MW SMR reactors could be on existing sites currently used for nuclear power stations to generate electricity for the National Grid.
The GMB Union has welcomed the news that Rolls Royce’ has written to several of England’s regional development bodies, as well as the Welsh Government, asking them to pitch for the manufacturing site, promising investment of up to £200m and the creation of up to 200 jobs in the area.
It is thought that Rolls Royce is looking at which areas have the necessary skills and training facilities, where there is suitable land available for the manufacturing facility and other infrastructure requirements.
GMB national secretary Andy Prendergast said: "This new fleet of small modular reactors is fantastic news for workers, energy users and the planet.
“Everyone in the energy business knows there can be no net zero without new nuclear. This is a massive step forward in cutting UK carbon.
"GMB members in the nuclear industry have been providing low carbon energy for more than sixty years.
“If politicians are serious about climate change - and a green economic recovery – we need to get spades in the ground for many more nuclear projects, both big and small, built right here in the UK.”
A spokesman for Rolls Royce said: "The development and growth of a UK nuclear manufacturing base is core to the deployment of Rolls-Royce SMRs.
"We have therefore initiated a process to identify a site for the first major factory installation, the Heavy Pressure Vessel factory. We look forward to working with LEPs and the Welsh Government to identify potential sites, an important step in delivering on our commitment to 80 per cent UK content for Rolls-Royce SMR deployment in the UK."