"He's just a precious old man. Everyone at the vet's office has fallen in love with him," Michelle Wacker, special needs director for the shelter, said to WESH-TV in Orlando.
After helping him overcome hookworms and whipworms, Sniffles was featured in a Christmas Eve profile aired by the TV station.
The story went viral and there has been an outpouring on social media with posters writing he is a "sweet old guy," "adorable" and one to "die for."
"The outpouring of support has been overwhelming and heartwarming," the shelter posted on its website. "Sniffles is going to be a-okay and we ask that you please set your sights on some of our other dogs in need."
Poodle and Pooch Rescue said it is sorting through 200-plus emails, voice messages, social media inquires and applications "to determine the absolute best and most suitable home for Sniffles."
The shelter found out Sniffles was originally from Puerto Rico, where he likely lost his nose due to trauma -- possibly from a pack of dogs.
He was rescued by a group known as Rabito Kontento, which is Spanish for Happy Tails.
Sniffles was adopted in Florida but he managed to continually escape from his new owners.
He eventually ended up as a stray captured by Orange County Animal Services and taken in by Poodle and Pooch Rescue, Wacker said.
"This morning I woke up and he was at the edge of my bed, staring at me, and he ran over and did a little twirl and started licking my face," Genesis Diaz, who has been fostering the dog, told WESH-TV.
Sniffles needs dental work and his appearance will improve.
"Ninety percent of the time, we can fix these dogs," Wacker said. "When we see a special needs dog that we know we can help, we move to bring it in. Otherwise, it likely faces euthanasia."
In Sniffles' case, Wacker said "he's a healthy dog. He just looks a little funny."