The report came as Russia's state-held Rosneft faced a deadline of Monday to either accept or reject the revised terms of its $16 billion (11.4-billion-euro) strategic alliance with the British energy firm.
An arbitration ruling this month forced BP to hand the Arctic exploration portion of the tie-up to its Russian joint venture. But Rosneft has previously rejected the idea of working jointly with TNK-BP.
The Wall Street Journal cited "people familiar with the situation" as saying that BP has revived previous efforts to buy out the four Russian partners who control half of TNK-BP.
The British company had previously offered $27 billion for the stake, according to previous reports. But the Russian billionaires have valued their share of BP's local venture at up to $40 billion.
The Russian partners have denied any interest in selling their stake. But some analysts suggest that they may use this opportunity to sell out because of inevitable future frictions with both BP and Rosneft.