Kaye, who has kept the pigs at a patch of ground near her house for six years, said they were hugely popular and caused no trouble.
But Allan Hess, whose home is next to the land, said it had become a living nightmare and he fears for his health if the animals are not removed.
The 67-year-old finance broker told the Liverpool Echo newspaper that pig waste from next door had stained his fence and footpath brown and compared it to living in Tudor England.
Kaye responded with an online petition called Save Suzie's Pigs which has been signed by almost 8000 people. A counter petition was then launched, which states: "Given that it is a residential area, we appeal for the pigs to be transferred to a more suitable area." That has been signed by several hundred.
"Just imagine having to live and share your life 24hrs a day seven days a week, smelling and inhaling, walking in the slurry from the pigs in your garden," it reads.
Kaye said she would be heartbroken if she was forced to move her kunekunes - Peppa, her piglets George and Nigel, and 7-year-old Sally.
Kaye has a caravan on the land where she keeps the pigs' bedding, food and straw. Each animal also has its own small wooden house as well as logs to scratch on and toys to play with. "Everybody loves them, I take them on walks to the park and people come from all over the place to see the pigs," Kaye said.
"They are intelligent, lovely animals that are no trouble and very clean as well."
A spokesman for Wirral Council told the Herald on Sunday there was no issue with the condition of the animals.
But he said: "The land does not have planning permission for the keeping of pigs. In addition, the structures and caravan on the land do not have planning permission.
"Ms Kaye has been advised to apply for planning permission. She has not as yet done so."
