President Vladimir Putin had held a surprise meeting with BP chief executive Robert Dudley and board chairman Carl-Henric Svanberg late on Tuesday, details of which were not made public by the Kremlin.
Conspicuously also present at the meeting was the Rosneft chief executive Igor Sechin, for long Putin's right-hand man on energy issues.
The Kommersant daily said that the sides were discussing BP selling its 50 percent stake in Russian joint venture TNK-BP to Rosneft in a deal that would be paid for half in cash and half in Rosneft shares.
Rosneft is already in talks with banks for a loan of $10-15 billion to finance the deal, the newspaper said. BP would receive a 12.53 percent stake in Rosneft with a market value of $8.6 billion.
The exact value of the cash component was not made clear.
BP has already said it is talking to Rosneft about the sale of its stake in TNK-BP, which it jointly owns with a group of Russian oligarchs. Although TNK-BP has been seen as the crown jewel of the British company, BP has nonetheless had a rocky relationship with the fellow shareholders.
If completed, the cash-share sale of the TNK-BP stake would mark another astonishing twist in BP's turbulent history of doing business in Russia.
BP and Rosneft in 2011 agreed a historic deal to tap Russia's vast Arctic energy resources which would have seen the British firm acquire 9.5 percent in the Russian giant and Rosneft 5 percent in BP.
However that deal collapsed after objections by the TNK-BP oligarch shareholders and the Arctic tie-up eventually went to ExxonMobil.
Kommersant said that the acquisition of a 12.53-percent stake in Rosneft as envisioned by this deal would make BP the second biggest shareholder in the firm after the Russian government.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional