Icelandic tycoon Thor Bjorgolfsson is selling his 65 percent option in BTC in a deal, estimated between 1.2 billion euros ($1.63 billion) and 1.3 billion euros ($1.77 billion).
The source, who declined to be named, said the deal was going into its final stage and would be closed soon.
"There are two companies -- one strategic and one financial -- that have been allowed to the final stage of the deal. A decision is to be taken very soon - in the next couple of weeks," the source told Reuters.
"For the strategic investor, Oger Telecom is closer to reality."
The other strategic bidder for the Balkan country's dominant fixed-line company was Turkish mobile operator Turkcell.
The source declined to name the financial front-runner, but confirmed Bjorgolfsson had chosen between Mid Europa Partners and a consortium of Texas Pacific Group and Warburg Pincus.
The 65 percent is currently held by U.S. Advent International that bought the stake in a 280 million euro privatisation deal in June 2004.
Novator, Bjorgolfsson's investment arm has said the sale would most likely be sealed by June 11 when the three-year ban on selling the majority package in BTC expires.
The company, which also owns the third mobile phone operator in the European Union newcomer, has forecast a 16 percent drop in its net profit to 111.6 million levs ($77.71 million) this year due to increased competition and dropping prices.
BTC ended 2006 with a net profit of 132.3 million levs on sales of 1.01 billion levs.