Large paw prints in the snow, farm animals savaged by mysterious predators and grainy photographs of huge feline silhouettes have fuelled the debate in the county for years.
But Gordon Buchanan, who comes to Telford next month, says modern technology makes such stories increasingly fanciful.
Gordon, whose touching documentaries with wild bears and wolves have led to comparisons with David Attenborough, says it is perfectly possible that panthers or pumas could be prowling the Shropshire countryside. But he says a lack of hard proof means the odds are now heavily stacked against it.
"I said about five years ago that, with everybody carrying mobile phones with cameras, we will soon have conclusive evidence if there were really big cats out there," he says.
"So far that has yet to materialise. Having spent some time with big cats, I know they are expert at concealing themselves and hiding, so it is possible. But in the absence of hard evidence, I think it's looking less likely."
The Shropshire Star recently revealed that Dyfed-Powys Police had been alerted to 14 reported sightings of big cats in the past five years, with many more reported in the West Mercia Force area.
However, aside from the corpse of an African Jungle Cat – found in Ludlow more than 25 years ago – there has been very little evidence to verify these stories.
"That's not to say that people are making stories up," says Gordon.
"A friend-of-a-friend showed me a picture of what they thought was a big cat, and I thought it looked like the real deal.
"It didn't look like a domestic cat, but when I saw where it had been taken, and paced out the distance, I realised it probably was a feral cat.
"But the way the image had been taken, unless you actually went out there and paced the distance you wouldn't have realised."
Gordon, 42, who made his name as the fearless cameraman on Big Cat Diaries in 2003, will tell his audience at Oakengates Theatre on March 3 about his encounters with weird, wild and wonderful wildlife, using his own footage and photographs.
But while he is not convinced about the stories of big beasts in Oswestry and Telford, he is a big supporter of reintroducing big cats into the British countryside.
"We should bring back as many of these lost species as possible," he says.
"The big thing at the moment is the reintroduction of the lynx. That's a fairly big cat, and I think within the next 10 years we will see these come back in the countryside."
The last wild lynx living in Britain is thought to have died around 1,500 years ago, but the Lynx UK Trust recently applied for permission to introduce a pair of the species into Scotland. If the trial is deemed to be beneficial to the natural environment, it is likely that similar schemes will be introduced in England and Wales.
Gordon Buchanan will be appearing at Oakengates Theatre on March 3 at 7.30pm.