EU competition commissioner Margrethe Vestager told the Daily Telegraph they had "grave suspicions" about Google's monopoly.
Last June she hit Google with a record £2.1 billion fine (US$3 billion) for giving its own comparison shopping service an unfair advantage on the search engine.
Google appealed against the European Commission's judgement, which would have meant it had to rearrange the way its searched algorithm ranks websites.
The California-based company is facing two other anti-competition lawsuits from the European Commission.
Most companies pay on average 24% corporate tax. Digital companies less than 10% in Europe. We propose to update our understanding of where to tax and what to tax — to ensure fair taxation also in our digital world @pierremoscovici #digitaltax— Margrethe Vestager (@vestager) March 21, 2018
Google Does Nine out of Ten Internet Searches in Europe
Google has a 91.5 percent share of the search engine market in Europe and Mrs. Vestager said the EU was not comfortable with this virtual monopoly.
Asked if the EU was considering forcing Google to break up into smaller companies, in a similar way to the banks after the 2008 financial crisis, she said: "It is important to keep that question open and on the agenda."
"We are not there yet but it is important to keep an awakened eye," she told the Telegraph.
Remember when Facebook, Twitter, and Google were going to change the world by depriving dictators of a monopoly of control over narratives?— Damir Marusic (@dmarusic) March 20, 2018
Mrs. Vestager, who has also faced down Apple and Amazon in recent months, said she feared Google would soon be indispensable for European businesses.
But the Danish commissioner was quick to insist the EU was not in the market of punishing companies for being successful.
"There is no ban on success in Europe. You get to be dominant and you get a special responsibility that you don't destroy the already weakened competition. We have proven their dominance in search and we have found they have misused this dominance to promote themselves and diminish competitors," Mrs. Vestager told the Telegraph.
Vestager Has Taken on Apple and Amazon
Mrs. Vestager, who has been in the job since 2014, has ordered the Republic of Ireland and Luxembourg to demand back taxes.
Google's troubles come just as another internet colossus, Facebook, is facing intense scrutiny for its activities.
Cambridge Analytica allegedly used the data while working for the Trump campaign.
Last week EU governments agreed a joint statement calling for "social networks" to offer "full protection of citizens' privacy and personal data."
Google says it is working on a plan to remedy the anti-competitive behaviour but last month some of Google's opponents said the only way to prevent the monopoly was by breaking the company up.