However, it had yet to receive an approach.
Jucy head of marketing Zoe McFarlane said the company was unaware of the problem before the Otago Daily Times raised the issue with her this week.
''This is the first time we are hearing the council has ... outstanding infringements.''
The council issued 2642 $200 camping infringement notices to tourists in 2014, but almost a third have not been paid.
Council regulatory manager Lee Webster considered the non-payment problem would be solved if rental companies billed tourists' credit cards - something the companies do not do, despite having the legal right to do so.
Ms McFarlane said Jucy dealt with camping infringements in the same way it dealt with its tourist customers' court fines and outstanding toll call accounts - by referring them to a company called Violation Management Services.
''They on-forward to the customer for payment.''
Ms McFarlane said it was not Jucy's responsibility to bill customers for fines. However, it was willing to discuss the matter with the council.
''We are always open to improving our processes, but we just need to be told what the problems are.''
Violation Management Services (VMS) is an American company with a post office box number in Tauranga.
A company representative contacted in the United States yesterday did not respond to an email request for more information about the company's operations in New Zealand.
VMS's website says it was established in 1991 ''to ensure vehicle owners are not held financially responsible for infringements committed by their customers''.
Queenstown Mayor Vanessa van Uden said yesterday the council had been involved with the company during a trial but the trial was ''not terribly successful''.
The problems over non-payment of fines was ''frustrating''.
The council had done its part with education and signage.
''We would have liked the rental car companies to play their part.''
She described Jucy as ''good operators'' and she would be happy to have discussions on the issue with both the company and the Government.
The ODT sought comment from Local Government Minister Paula Bennett yesterday.
She replied the matter had not been raised with her previously and she did not wish to comment until she had had a chance to investigate.
