Two years before her 1996 divorce, but after her separation from Prince Charles, Diana was spotted driving the young Princes in the green car on several occasions, making it one of the auction's star lots.
Until the auction, which takes place on 29 June at Blenheim Palace in Oxford, the car has been put on display at the Grange St. Paul's Hotel, London.
"This is an extraordinary opportunity to own a piece of royal history." said Chris Routledge, the managing director of Coys. "We have put a guide price on the car of between £20,000 and £25,000 but we have no idea what it will go for.
"Although we had not formally released the fact that the car was for sale until now, we have already had enquiries from around the world and particularly from America."
The four-seater vehicle is in immaculate condition, with only 21,000 miles on the clock.
Those visiting the car at the Grange St. Paul's Hotel will be able to leave a sealed bid for the auctioneer at Blenheim Palace in advance of the auction itself.
The hotel and auctioneer Coys are also collaborating to organise a competition where the winner will be driven in the car at Blenheim and treated to lunch before the auction takes place.
"We are delighted that potential purchasers and the public will have a chance to see this iconic car on display at the Grange St. Paul's," said Claire Farrington, Partnership Manager of Grange Hotels. "[The hotel] is just a few yards from St. Paul's Cathedral which holds such an important place in the history of the British Royal family."
Car experts Coys are no strangers to selling high-profile vehicles. In January Freddie Mercury's Rolls Royce sold at auction for six times its guide price and an auction in December 2011 saw an Aston Martin ordered by Beatles' star George Harrison make £350,000.00 after fierce bidding from around the world.