The Financial Times said European officials have requested Luxembourg provide documents relating to Amazon's tax affairs, putting it in line to join Starbucks, Apple and Fiat as targets of the investigation.
The probe announced last month is to determine whether tax arrangements offered by Ireland, Netherlands and Luxembourg give the companies an unfair competitive advantage and therefore amount to illegal state aid.
The European Union has no jurisdiction over national tax policies, a cherished prerogative of member states, so the probe is strictly limited to rules governing free competition.
Contacted by AFP, a spokesmen for the Competition Commission said it was "entirely premature to speculate on whether new investigations could target this or that specific company in the future".
"The Commission continues to gather information about certain tax practices in several member states in order to assess the situation from the point of view of EU state aid rules," said spokesman Antoine Colombani.
Apple and Starbucks - as well as Amazon - have come under intense pressure from politicians and campaigners over their tax dealings.
(Also see: Booksellers Score Some Points in Amazon's Standoff With Hachette)
Critics and opponents say so-called "sweetheart" deals allow the companies to move billions in earnings from higher-taxed countries to lower-taxed ones, minimising their payments.
The probes are far-ranging and include a deeper look into so-called "tax rulings", where a company negotiates a tax arrangement before choosing where to domicile its activities.
The investigation also focuses on the use of transfer pricing, an accounting technique that allows units of international companies to pay 'royalties' to another unit of their business.
The mechanism - possible under carefully crafted laws in Ireland, Netherland and Luxembourg - allows companies to post losses in countries with higher tax rates and move profits to where they will have to pay lower rates.
(Also see: Hachette Seeking Amazon Terms That 'Value' Authors and Publishers)
Ever since the 2008-09 financial crisis, multinationals have faced increased scrutiny on tax matters.
The OECD, working under the auspices of the G20, has embarked on a reform campaign to stop multinationals from exploiting loopholes and divergent tax regimes.Get your daily dose of tech news, reviews, and insights, in under 80 characters on Gadgets 360 Turbo. Connect with fellow tech lovers on our Forum. Follow us on X, Facebook, WhatsApp, Threads and Google News for instant updates. Catch all the action on our YouTube channel.