The 40 kg (84 lbs) male beaver jumped a fence in October during floods and made his escape from a nearby farm along with two female beavers, the Plymouth Herald said.
His two companions were recaptured by owner Derek Gow, who runs a conservation program in the region to try and reintroduce the beaver to the U.K.
However, the male, nicknamed Igor by British papers, has eluded all attempts to catch him and is now felling trees along the River Tamar to try and entice a female mate, but bearing in mind the beaver was hunted to extinction in Britain some 400 years ago, he is on a hiding to nowhere.
"I know where he is," the Herald cited Gow as saying. "But he's occupying a territory of probably one kilometre in length."
Beavers mate for life so Gow said he would need to use a "honey trap" to try and capture the elusive-furry tree eater.
"We've got traps being made up at the moment. Using the scent from one of the female beavers, we'll be able to catch the male beaver fairly quickly."
The conservationist has some 24 beavers at his farm under license as part of a project to release four families from Norway, Igor is from Bavaria, in Scotland in the spring.
Gow defended the damage to trees in the region, saying it was natural, "They do chop trees down, but you've got to remember that this is a native animal to this country."
