The grey and white cat, known variously as Rudolf or Bruno despite being female, can often be seen sitting near the notorious "Arbeit macht frei" ("Work sets you free") sign at the entrance to the camp.
She has seemed unperturbed by an unusually cold winter in Poland that has seen night temperatures dip as low as minus 34 Celsius (minus 29 Fahrenheit).
The museum that runs the camp has rejected a call from the group For Animals to build a cat shelter, saying other animals also live at the site and that visitors are its main priority.
"All we asked for was to erect a shelter, but we were refused," said Joanna Zaremba of the For Animals foundation.
A museum employee tried in vain to give the animal a home.
"The cat was not used to being indoors and the employee had to let her out to feel free. She came straight back (to the camp) like a boomerang, back to the 'Arbeit macht frei' gate," said Adam Cyra, another member of staff.
The cat is believed to have arrived at the camp about six months ago and started to attract the attention of visitors after Polish newspapers and websites reported on the animal's attachment to the site and the campaign to build a shelter.
"I came especially to see this cat as I've heard so much about it in the local media," one Polish visitor told Reuters Television. "I'm ready to adopt the cat and give her a home."
While the cat has been staying near the entrance, a gang stole the "Arbeit macht frei" sign. Polish police later recovered the sign, cut into three pieces, and arrested five suspects over the crime.
Up to 1.5 million people, mostly Jews, perished at Auschwitz during the Nazi occupation of Poland in World War Two. The site, near the town of Oswiecim in southern Poland, received more than one million visitors last year.