Google is said to be negotiating a tax settlement with France worth three times more than it paid the British Exchequer even though it employs thousands more staff in the UK.
The UK arm generates about three times as much revenue as Google France and employs four times as many people.
The Times reported that French officials are chasing the internet giant for €500m (£381m) over a similar tax avoidance structure to the one it used in the UK which has caused controversy.
As the internet giant expands its operation in the UK, it and HMRC are in the firing line from campaigners after Google settled its tax bill with the British government for £130m over 10 years, compared with the company's $5.6bn (£3.9bn) annual UK revenues.
Downing Street distanced itself from Chancellor George Osborne's claim that the £130m agreement was a "victory" for the taxpayer as sources at the National Audit Office told the Daily Mail that it would be investigating the deal.
Despite HMRC spending six years investigating Google, The Times reported that tax officials never challenged the company's claim it had no "permanent establishment" in Britain. This allowed it to book its sales through an Irish subsidiary from where profits were diverted to the tax haven of Bermuda.
Meg Hillier, chairwoman of the public accounts committee, told the newspaper it was shocking that HMRC had failed to challenge Google on this point even after her committee had handed investigators evidence from two whistle-blowers that appeared to undermine the company's claims.
"It beggars belief that they didn't challenge that basic question. It underlines my real concerns about HMRC not keeping up with the big guys," she said,
The committee took evidence in 2012 from two former Google employees who claimed that many of its 2,000-plus London staff made sales and developed products although this was contradicted by Matt Brittin, Google's vice-president, who had told the committee no one in Google Ltd in the UK was selling Google products.
In February, officials from HMRC and Google will face questioning from the committee.
In a statement, Google said: "After a six-year audit by the tax authority we are paying the amount of tax that HMRC agrees we should pay. Governments make tax law, the tax authorities enforce the law and Google complies with the law."
Google plans to employ up to 5,000 people in new £1bn headquarters in London.