An unofficial world record was set when 40.45 kilograms of wool was removed from the overgrown sheep, dubbed Chris, in a risky operation on Thursday.
ACT RSPCA chief Tammy Ven Dange said since Chris hit the headlines, the animal welfare organisation has been inundated with offers from people wanting to look after the sheep.
"We've had hundreds of people requesting that," she said.
Interest has even stretched beyond Australia, with offers of a new home received from people living in England and Vienna.
But the RSPCA said an overseas move was not on the cards for Chris, with the sheep likely to remain in the ACT.
"I think we've found him a nice little obscure farm though that hopefully he can live out his life without anyone knowing his true name, " Ms Ven Dange said.
The sheep is still undergoing daily vet checks, but has been making improvements.
"He is quite skinny so we're doing our absolute best to fatten him up as quickly as possible," Ms Ven Dange said.
"I think his back legs will probably be a little bit awkward for the rest of his life because he was carrying that much extra weight for so long.