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.

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.

As well as shocking VW customers, the scandal has stunned investors in the car maker.

The BBC has learned that debt products issued by Volkswagen are under review by the European Central Bank (ECB).

The ECB has been buying debt products from big companies, including VW, as part of its scheme to boost the eurozone economy.

But following the admission by the carmaker that it cheated emissions tests, the ECB is reviewing its purchase of debt from VW.

In particular, it is examining debt backed by loans to buyers of VW cars.

The products, known as asset-backed securities, have been popular investments as they offer a relatively high rate of return in an era when interest rates are low.

Such debt is also very important to car makers and allows them to finance loans to customers.

The indication of concern by the ECB will be a worry for other investors in that debt and could affect VW's ability to raise money.

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 a similar ban in the UK.

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.

Source: BBC