Having arrived at Bridgnorth Veterinary Centre at 11 weeks old, Digby was found to have a congenital heart condition called Patent Ductus Arteriosus (PDA) and was brought in to be put to sleep.
But following expert advice, the veterinary centre is now fundraising £3,400 to provide the 13-week-old collie cross-breed with the operation he needs to save his life.
Claire Upton, of the vets in Whitburn Street, said the black and white furry friend has already been referred to a cardiology specialist in Hampshire for diagnosis, and experts believe they can treat him.
"He's really friendly and so playful, but he does tire very quickly, which is a symptom of his condition," Claire said.
Explaining Digby's condition, she added: "In a normal heart, blood will be pumped out of the right side of the heart to the lungs to pick up oxygen.
"Before birth the Ductus Arteriosus plays a very important role; due to the lungs not yet working it diverts the blood. Before the puppy is born the Ductus Steriosus should completely closed so that the blood can be redirected to the lungs before returning back to the heart.
"In some cases such as Digby’s, the closure of the Ductus Steriosus fails or is incomplete leaving it patent and specialist veterinary surgery intervention is required to close the PDA as soon as possible before irreparable damage to the heart muscle is suffered."
The surgery will involve a specialist cardiology surgeon using a device and a catheter through an artery in the leg.
Claire added: "However, whilst we can help with the cost of his care, the implant needed and surgery by a specialist is not without some expense.
"We are now relying on donations to help fund his operation to save his life. Any contribution would be greatly appreciated, as you can see he is way too cute for us to give up on."
To donate to Digby the dog's surgery, visit gofundme.com/f/help-digby-have-his-life-saving-operation