The company is battling the database giant Oracle in a trial in California, to try and keep to a minimum the damages it will have to pay for using code from Oracle's Java software in its Android mobile operating system. That case has been going on since 2010.
A report in the British newspaper, The Telegraph, said the EU was likely to act next month, before the summer break, bringing to a head a seven-year investigation into Google's market tactics.
The maximum fine possible under EU law is €6.6 billion, a tenth of Google's annual sales.
Apart from the fine, the report said Google would be prevented from manipulating search results to favour itself and harm its competitors.
It said that while the previous EU competition commissioner Jaoquin Almunia had tried to make a deal with Google without bringing formal charges, his successor, Margarethe Vestager, had taken a much more aggressive approach to the issue and whatever fine she levied would be a slap in the face to Google's argument that online competition was alive and well because Amazon and eBay are thriving.
A Reuters report said that there had been three failed attempts to settle the issue and bring about a compromise solution and that Google was unwilling to do anything unless the EU changed its approach.
The biggest fine levied by the EU for monopolistic behaviour so far has been the €1.1 billion it imposed on Intel in 2009.