The car, built in 1934 is expected to fetch £8.5 million at an auction being conducted by the Rolls-Royce Museum at Muhlheim in Germany.
Known as the Star of India, the car has a number of features which were considered unique at the time including headlights which are controlled by the steering wheel and track the vehicle's progress in the road.
Similar technology – now called "adaptive curve lights" – is featured on a number of cars today including BMW's and Mercedes.
When it is sold the price raised for 1934 Phantom II 40/50 HP Continental "All-Weather Convertible" is expected to exceed the £7.2 million paid for a 1957 Ferrari 250 Testa Rossa at auction in May.
It is part of a collection belonging to Hans-Gunther Zach's private collection, and bids are being entertained until September 15.
Zach is accepting bids on 24 other rare Rolls-Royce's and three Bentleys including a 1926 Rolls-Royce 40/50 HP Phantom I Open Tourer, built for the Maharaja of Nanpara in India and known as the "Aluminium Sculpture" because of its natural aluminium body and chassis.
Also for sale is a Phantom II Cabriolet "Hunting Car" built for the India's Maharaja of Rewa. Designed to hunt India's tigers, the "Hunting Car' has a specially designed gun rack built into the chassis.