The trust said the next stage follows its feasibility study, which identified the two locations and found 91% of the surveyed public were in favour of beavers returning to Gloucestershire.
Prior to being hunted to extinction about 400 years ago, beavers were widespread across Britain for more than two million years.
Dr Amy Fitzmaurice, species recovery officer for Forestry England, said the beavers in enclosures in the Forest of Dean were “making a real difference” by restoring wetlands, creating habitat, and slowing the flow of water.
“Across the country, beavers are starting to return to the wild too, but that kind of change takes time and careful planning,” she said.
“By working with Gloucestershire Wildlife Trust and other partners, we’ve been able to look closely at what beavers could mean for the Severn catchment, the opportunities they bring, as well as the challenges.”