The German operator is reportedly looking to secure an additional 10% in the Greek incumbent from the heavily indebted Greek government.
A report from a local newspaper on Saturday claimed that both sides were in “advanced talks” and were “ready to shake hands”.
The 10% of OTE which Deutsche Telekom is looking to acquire is divided between Greece itself, which owns 6%, and state-run pension fund IKA which owns the remaining 4%.
Deutsche Telekom bought its existing 40% stake in OTE in 2008, at which time it also secured a right of refusal if Greece decided to sell any further shares.
Greece has been pursuing a multi-billion privatisation strategy in a bid to reduce its significant debt but has previously been unwilling to part with its stake in OTE.
However, with privatisation revenues falling below its €22 billion target, the country has had to reconsider its options.
Earlier this month Deutsche Telekom announced it was looking to invest more money into OTE which is worth an estimated €6.1 billion on the Athens Stock Exchange.