BMW has restored the BT52 in its collection as part of its celebrations of the 30th anniversary of its world championship victory with Piquet and Brabham in 1983.
The BMW-powered car, the work of design legend Gordon Murray, will be present at the Festival of Speed on July 11-14 and the German manufacturer is already talking to Piquet about driving it up the hill.
BMW Motorsport boss Jens Marquardt said: "A car like this has to be running and it is good to remind ourselves and our fans of our heritage."
He explained that contact had already been made with Piquet through long-time BMW Motorsport engine boss Paul Rosche, who masterminded the German manufacturer's 1.5-litre turbo engine programme in the 1980s.
The BT52, chassis #1, and its four-cylinder powerplant have been subject to a ground-up restoration at BMW Classic in Munich, which began last October.
The car was Piquet's spare at seven grands prix over the course of the season and was also raced by Riccardo Patrese at the Belgian and Canadian grands prix.