It has been signed by more than 16,000 people so far.
According to reports, Ms Price, 43, recently ‘gave her daughter Princess’ puppy’ away to a crew member working on her reality show.
The mum-of-five, who lives in West Sussex, is the owner of a number of animals, however a few have died while in her care in a series of tragic accidents.
Including two dogs who have been run over, one who suffocated while trapped under a chair and more.
The petition was launched on change.org by an account called ‘ban the fur don’t wear animal fur’.
It says: ‘The neglect seen on her show my crazy life. Cat poo with mold growing on it.
‘Dog poo just left on the floor. Clothes dumped all over the place.
‘She jokes about her mucky mansion. But it ain't a joke that animals are dying.’
Animal charity PETA's director, Elisa Allen said: ‘Given her track record with animals, several of whom have died in her 'care,' it would be irresponsible and reckless for Katie to be allowed to acquire another one.’
A representative for Ms Price told the Mirror: ‘It has been well documented that Kate is an avid pet lover and these incidents have occurred however, Kate would be more than happy to sit down with Elisa Allen, director of PETA, to discuss her concerns.’