"As far as our country is concerned, back taxes concerning this company amount to EUR 1.6 billion," the official, who spoke on condition of anonymity, said.
A spokeswoman for Google France declined to comment on the amount when contacted by Reuters, saying only that the company obeyed tax rules in all countries where it operated.
The finance ministry also declined comment. An unsourced 2012 media report mentioned a claim for EUR 1 billion by French authorities, which Google denied at the time.
Shares in the company were down 1.8 percent in early New York trade, broadly in line with the Nasdaq average.
French tax authority usually issues at least one preliminary assessment before its final assessment, which can be challenged in court if not accepted, tax advisers say.
Earlier this month, Finance Minister Michel Sapin ruled out striking a deal with the US search engine company as the British government recently did, saying the sums at stake in France were "far greater" than those in Britain.
Google reached a GBP 130 million settlement with British tax authorities for the period since 2005, which British lawmakers criticised on Wednesday as "disproportionately small".
France, Britain and other countries have long complained at the way Google, Yahoo and other digital giants generate huge profits in their countries but have their tax base in countries such as Ireland, where corporate tax rates are far lower.
But the complaints have made little legal headway because EU tax law protects companies against paying tax in a country where they do not have what is termed a "permanent establishment".
© Thomson Reuters 2016