The warning from internal engineers as far back as 2011 is said to have surfaced from VW's internal investigation into the scandal which has rocked the company, German newspaper Frankfurter Allgemeine Sonntagszeitung claims.
A separate report in Bild am Sonntag said the investigation had also turned up a warning from Bosch from as far back as 2007. The company, which supplies parts to VW, said its software should only be used for company tests and not for normal driving, according to the report.
Volkswagen could not be reached for comment at the time of publication.
More than 11 million cars have been affected by the misleading emissions testing, forcing chief executive Martin Winterkorn to resign and cutting billions from the value of the company as at least 10 countries launched investigations into VW.
According to several reports, the European Central Bank has suspended buying any loans backed by Volkswagen from its bond-buying programme, in the latest fallout from the scandal.