Government officials from both countries discussed closer cooperation in transportation, including establishing a joint airline, when Prime Minister Tayyip Erdogan visited Moscow this month, the official said on condition of anonymity.
The size of the stakes that each state-run carrier would hold has not been decided, nor which aircraft would be used, he said.
Haber Turk newspaper reported that both airlines would own a 50 percent stake in the passenger airline that will use Russian-made Sukhoi jets that carry between 80 people and 95 people.
Russia and Turkey will ease visa restrictions on travelers to encourage tourism, the daily said. Some 3 million Russian tourists visit Turkey each year, and the new airline is likely to lift those numbers, it said, citing Transport Minister Binali Yildirim.
Turkish Airlines' board has not made any decision on the issue, spokesman Ali Genc said, without elaborating.
No financial details of the venture were available.
Shares in Turkish Airlines were unchanged at midday, outperforming the main index, which declined 1.55 percent.
The Istanbul-based carrier flew 25.1 million people last year. It had revenue of 2.09 billion Turkish lira ($1.4 billion) in the third quarter of 2009.
Aeroflot carried 8.015 million people in the first 11 months of 2009, according to Interfax. It had nine-month sales of $2.46 billion.
Sukhoi said last month that a delay in the engines has indefinitely put off deliveries of the Superjet 100, its first production of civilian aircraft since the fall of the Soviet Union.
Sukhoi, which makes fighter jets, is developing the Superjet 100 with shareholder Italian aerospace and defense group Finmeccanica SpA. The engines are being produced by Russia's Saturn with France's Safran, while Thales is involved in avionics.
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