RSPB Scotland offered some of its own 80 nature reserves as potential sites following last month's conclusion of the Scottish Beaver Trial, run by Scottish Wildlife Trust and the Royal Zoological Society of Scotland, in Knapdale Forest in Argyll.
The beavers, which began to be introduced five years ago, now range over a territory equivalent to 120 football pitches. Between May 2009 and September 2010 16 Eurasian beavers were released in the woodland, near Lochgilphead.
Duncan Orr-Ewing, head of species and land management at RSPB Scotland, said: "Beavers are incredible mammals that have an important role to play in our countryside. We urge the Scottish Government to make way for further projects to bring this remarkable species back to our countryside."