The $5bn offer comes weeks after the two companies buried the hatchet over Rolls-Royce Motors and agreed to split the Rolls and Bentley brands.
Piech made the extraordinary offer in an interview at the Hanover truck show with the prestigious German newspaper Suddeutsche Zeitung.
BMW shares rose 77 marks, or 6.3p per cent, to 1,302 marks and VW shares rose by 1.5 marks, or 1.1 per cent on the news.
Significantly, Suddeutsche is the main newspaper in Munich, BMW's home town, leading some analysts to speculate that the remarks were deliberately aimed at sowing dissension within the Quandt family, the 46 per cent shareholder in the Bavarian company, whose consent would be needed for any merger deal.
The move appears to have been prompted by VW's concerns that it may be left behind following the giant DaimlerChrysler merger earlier this year. Piech has failed to strike a deal with either Volvo or Scania, the Swedish truckmakers.
BMW yesterday refused to comment on Piech's remarks insisting that the issue was a matter for its shareholders.
But the BMW management board chairman, Eberhard Von Kuenheim, said when the idea of a defensive share swap between the two companies was first mooted by Piech that he believed the conditions were not right.
Von Kuenheim is very close to Joanna Quandt, matriarch of the BMW clan. She is the widowed third wife of Herbert Quandt who bought 30 per cent of the company in 1960 at a time when it was virtually on its knees.
Piech has clearly not been put off. Analysts said he may have been encouraged by the rumblings that followed a DM3bn rights issue earlier this year which suggested that the younger generation of Quandts were not as committed to the company as Joanna.
The BMW management, say observers, is also getting more chary about being able to finance future model development on its own, particularly now it is finding turning Rover around a harder task than it originally assumed.
The Quandts were recently on the receiving end of a similar approach from the Agnelli family who control Fiat, the Italian carmaker. They are also increasingly nervous about the company's long-term future should the DaimlerChrysler deal spark a wholesale shakeout in the industry, particularly if followed by another downturn in car sales.
One analyst said: "BMW is making hay at the moment. But this is a company which thinks long-term, 10 to 25 years. Scale is important in this industry.
"If they were to put themselves up for sale, you would be trampled in the rush. But they may be wondering that if they hang about too long the other attractive partners may have all paired off."
The precise breakdown of the Quandt family shareholding is a closely guarded secret. But a German newspaper claimed several years ago that Joanna has 17.9 per cent, while Stefan, Herbert's son owns 18 per cent. Joanna's daughter Susanna Klatten owns13.2 per cent.