AAR, the vehicle used by a quartet of Russian billionaires to hold the other half of TNK-BP, is willing to raise its offer to BP from the original $10bn (£6.2bn) for a 25 per cent stake.
The group hopes to make a bid before its 90-day window expires in mid-October, after which TNK-BP is open to a rival approach from state-owned oil group Rosneft.
A source close to the oligarchs said they would likely make an all-cash offer, compared to a mix of shares and cash on the table from Rosneft.
AAR could also ditch its various legal battles against BP as part of a deal to buy out its partner, the source added.
BP said in June that it planned to sell some or all of its lucrative but troublesome TNK-BP venture.
It has been in discussions with AAR since then, but also started talks with Rosneft in July.
BP is required to conduct 90 days of good faith negotiations with AAR under the pair’s shareholder agreement.
TNK-BP has paid out $19bn in dividends since BP set up the venture in 2003, but is at the centre of a sprawling dispute between its owners over management and exploration rights.
Some analysts say that BP is likely to prefer Rosneft as a buyer. The prospect of acquiring equity in the Russian oil major could serve as a “poison pill” takeover defence for the London-listed firm, which is still feeling the effects of the 2010 Macondo oil spill.
But others are sceptical that Rosneft and AAR would agree to work together, given the oligarchs scuppered last year’s £10bn tie-up between Rosneft and BP.