A judge ordered the rings to be sold online through West Auctions following Brown's August 2008 Chapter 7 bankruptcy filing. The minimum bid was set at $19,000.
"People figure that here's this guy ... he's played in the NBA, he just got fired (as a coach), he's broke, and here he is giving up his championship rings," he told the paper. "That hurt me because those (rings) mean a lot to me."
Among the listed bidders on the West Auction Web site was Estee Portnoy, the longtime publicist for Bulls legend and former Brown teammate Michael Jordan.
Portnoy declined to say whether she was bidding on Jordan's behalf. Her final bid came Tuesday, topping out at $40,000.
"I was just bidding to win," said Portnoy, reached by phone Thursday afternoon. "I didn't win."
Portnoy also declined to say whether she was bidding with the intent of returning the rings to Brown.
"I didn't have any special motivation," she said. "I'm just disappointed I didn't win."
The Sacramento Bee also reported May 5 that Brown was informed he could not regain the rings by way of a third party through the auction. He was told that if he couldn't reclaim the rings, the Bulls could replace them.
Bidding was anonymous, but because it was a public sale conducted on behalf of the bankruptcy court, the name of the final bidder will eventually be released as part of public record.
Brown, a guard on the 1996, 1997 and 1998 Chicago Bulls championship teams, was fired as a Sacramento Kings assistant coach in April.
Click here to see photos of Randy Brown's championship rings.