The oil company said in a statement on Friday that it had received "unsolicited approaches" and had notified its partner, Alfa Access Renova, a group of four Soviet-born billionaires, of its intention to pursue a potential sale.
A spokesman declined to say which parties had made the approaches but, given the Kremlin's desire to exert influence over the oil sector, suspicion is likely to fall on state-backed players such as Rosneft and Gazprom.
On Monday one of the billionaires, Mikhail Fridman, resigned as chief executive of TNK-BP T citing a breakdown in relations with BP.
BP sources said they believed the move was a tactic to force the company to buy out AAR's stake in the venture.
BP formed TNK-BP with AAR in 2003 to expand into Russia, one of the few major resource-holders where foreign oil companies could invest.
It has been a huge financial success for BP, yielding billions of dollars more in dividends than it invested in buying its interest.
However, it has been a bumpy ride, prompting investors to attach a significant discount to the stake.
Shortly after the venture was formed, Russia became more hostile to foreign and private sector investment. The Kremlin's preference to reserve larger fields for state-controlled groups has limited TNK-BP's ability to expand in Russia.
Meanwhile, BP has been locked in periodic spats with its co-owners that have led to worries that BP could lose its interest with little or no compensation