Robert McDougall, a 25-year-old arts student from Melbourne, found it "mildly outrageous" that the key was being sold.
"I found it pretty insulting," he told The Age.
"I think there have only been about 33 given out in the last 30 years and they have gone to people like the Dalai Lama."
Mr McDougall has written to the seller explaining his reasons for not honouring his $92,030 bid.
The key's sale outraged current Adelaide Lord Mayor Stephen Yarwood and former Mayor Steve Condous, who presented the key to Cher in 1990.
Cher herself claimed to be unaware of the sale, stating on Twitter last week: "Im upset 2& trying 2get2 bottom! I think my office fkd up?"