Frankfurter Allgemeine Sonntagszeitung says the warning emerged during VW's current investigation into the scandal.
Separately, Bild am Sonntag said the internal inquiry had found that parts supplier Bosch had warned Volkswagen not to use its software illegally.
Volkswagen told the BBC they would not comment on "newspaper speculation".
Last week VW apologised for cheating on emissions tests in the US. Some 11 million VW diesel cars built since 2008 are affected by the scandal.
They had devices which could detect when the engine was being tested and could change the car's performance to improve results.
Volkswagen: The scandal explained
Citing unidentified sources, Bild said Bosch had warned Volkswagen as early as 2007 that its software should only be used in company tests and not for normal driving.
Last week VW's chief executive Martin Winterkorn was forced out over the scandal and replaced by Matthias Mueller, the former head of Porsche.
On Friday Switzerland temporarily banned the sale of Volkswagen (VW) diesel-engine models which could have devices capable of tricking emission tests.
It said the move could affect 180,000 cars - not yet sold or registered - in the Euro5 emission category.
The Swiss authorities have also set up a taskforce to fully investigate the issue.
A spokesman for the British department for transport said there were no plans for ban in the UK.
Countries investigating emissions-rigging scandal
United States: Scandal emerged following findings by the Environmental Protection Agency. Justice Department and New York regulators have launched criminal investigations
Germany: Transport Ministry to send fact-finding committee to Volkswagen
United Kingdom: Vehicle Certification Agency to re-run lab tests and compare with "real-world" driving emissions
Switzerland: Task force set up to investigate
Italy: Spot checks to be carried out on at least 1,000 diesel vehicles, transport minister says
France: Random checks on 100 diesel cars aimed at "ensuring the absence of fraud", says Environment Minister Segolene Royal
South Korea: Environment Ministry to investigate 4-5,000 Jetta, Golf and Audi A3 vehicles, could extend to all German diesel cars if problems found
Canada: Environmental Agency investigating some 100,000 Volkswagen and Audi diesel cars
Norway and India opening fraud investigations
The US Department of Justice (DoJ) told the BBC that it would join the US Environmental Protection Agency's (EPA) investigation into VW.
The EPA's findings of the scandal cover 482,000 cars in the US only, including the VW-manufactured Audi A3, and the VW brands Jetta, Beetle, Golf and Passat.
But VW has admitted that about 11 million cars worldwide are fitted with the so-called "defeat device" - 2.8 million of them in Germany - and further costly recalls and refits are possible.
Half of the company's sales in Europe - VW's biggest market - are for diesel cars.
VW shares plunged around 30% in the days after the scandal broke.
