The Jeep had already drawn bids of up to $15,000 by Thursday, with the auction ending March 18. The bids had not yet met the reserve price set by eBay subsidiary Kruse International, which is acting as an agent for the Jeep's anonymous owners.
Under eBay rules, Kruse is not required to sell the Jeep unless bidders meet or exceed its secret reserve price.
The Jeep Wrangler has a manual transmission, six-cylinder engine and 35,884 miles on its odometer.
Also up for sale is a letter Kennedy wrote to Vernon Jordan, an adviser to President Clinton, seeking a job in Washington, D.C. The opening price for the letter is $8,500.
Kruse is also auctioning a notepad on which Kennedy wrote concerning the launch of George magazine, and a card that notified Kennedy that he had passed the New York state bar exam. The opening prices on the two items are $3,900 and $2,000, respectively.
The auctions are among a series of celebrity-related auctions on eBay.
Last December, Kruse auctioned a BMW that had belonged to Kennedy's mother, Jacqueline Kennedy Onassis, for $57,100 on eBay Motors.
On March 22, eBay affiliate Butterfields will auction several items related to Marilyn Monroe, including the images and copyrights for several nude photos taken of Monroe early in her acting career. Bidding will start at $350,000 for the auction.