Sources familiar with the matter told the Wall Street Journal that Deutsche and Fon have already signed a letter of intent but with the size of the stake and its value not yet decided.
Fon offers over 11,000 hotspots in Germany and over 600 million worldwide through partner networks.
If an acquisition were to go ahead it would be a boost to Deutsche Telekom’s strategy of increasing mobile data revenue.
Deutsche Telekom CEO, René Obermann, predicted at the end of last year that the company’s biggest growth in revenues will come from mobile internet usage, achieving approximately €10 billion by 2015.
Fon has agreements with several major European operators in Belgium, France, the UK, Poland, the Netherlands and Portugal.
The company’s investors include Atomico, British Telecom, the Coral Group, Google, Index Ventures, Sequoia Capital and Skype.