The Financial Times and The Wall Street Journal both cited sources familiar with the case and said the EU was getting ready to announce the results of the first of three anti-trust cases into the company's business practices in Europe.
The reports said the fine could exceed the €1.1 billion imposed on Intel in 2009.
It also said that its "preliminary view (was) that the company has abused its dominant position by artificially restricting the possibility of third-party websites to display search advertisements from Google's competitors".
In May, a report said the EU was likely to act this month, ending the seven-year investigation.
The EU has two other investigations into Google going on: one is looking at whether it unfairly blocked competitors from sites that use its search bar and ads.
A third case is scrutinising how Google pays and limits mobile phone providers who use the search company's Android software and app store.
A Reuters report last month said three attempts had been made to settle the issue and bring about a compromise, but that Google was unwilling to shift unless the EU altered its approach.