German magazine Der Spiegel said last week that Piech, ex-chairman of the Volkswagen supervisory board, had incriminated former group CEO Martin Winterkorn, who had "knowledge of the diesel fraud earlier than admitted".
"All affected members of the executive committee of the supervisory board, acting independently of each other, have unequivocally and emphatically rejected all assertions made by Ferdinand Piech as untrue," Volkswagen said in a statement, threatening possible legal action against him.
Piech, a grandson of VW's founder who served as CEO between 1993 and 2002, was forced from his position as chairman of its supervisory board in April 2015 after an ugly leadership battle with his former protege Winterkorn.
According to Der Spiegel, Piech told German investigators that he himself learned from an informant in February 2015 that the company had a "big problem" in the United States.
The source told Piech that US authorities were looking into its use of manipulating software to dupe pollution tests and had passed on their findings to Volkswagen.
Piech then asked Winterkorn about it, who assured him that no such document from US officials existed, according to Der Spiegel.
After steering Volkswagen from 2007 to 2015, Winterkorn resigned days after VW admitted in September 2015 that it had installed so-called defeat devices in 11 million diesel engines worldwide to make the cars seem less polluting than they were.
Winterkorn has always insisted he knew nothing of the scam before it became public knowledge.
Prosecutors in the German city of Brunswick however announced at the end of January that they were investigating Winterkorn for fraud, saying they had "sufficient indications" he knew about the cheating earlier than he claimed.