A bidding war has broken out for the fleece from a Tasmanian sheep which made international headlines last week vying for the title of the world's woolliest.

Dubbed Shaun, the runaway sheep found at a farm in the state's midlands was shorn for the first time in six years last Thursday.

The fleece weighed in at 23.5 kilograms, just short of the world record held by New Zealand sheep Shrek.

Owner Netty Hazell said it was worth only $200 but she had been offered a thousand times that amount.

"We've had an offer from Japan, we've had an offer here from Tasmania and at this stage, we also have an offer from the Geelong Wool Museum in Victoria," she said.

"They're offering in the thousands."

There had been initial concern that Shaun might not have survived the shearing, with his owners giving him a special coat to guard against the temperature drop he experienced.

But Mrs Hazell said he was doing well and even had a makeover.

"He's doing extremely well, he's learnt that he can run and he's enjoying himself," she said.

"He had his coat removed for the first time yesterday since shearing and he's put on some weight.

"We've done his toenails, so he's now starting to walk a bit better and he's just a happy sheep."

It is believed Shaun fled a bushfire on an east coast farm six years ago and had been wandering the bush until the Hazels stumbled across him on their property last week.

After his ordeal, Shaun may now be destined for the rural "celebrity circuit".

The public will get their first glimpse of the hefty fleece when it goes on display at next month's Royal Hobart Show.

Shaun, who now has his own Facebook page, may also make the trip south.

"We're organising now with the Hobart show committee to have his fleece down there, we're looking at also spinning a little bit so the general public can see that, and there's some whispers that he may make an appearance," Mrs Hazell said.

Despite being inundated with requests to buy the fleece, the Hazells are hanging onto it for now.