BP's Russian joint venture would buy the BP stake and then swap it for a 10 percent stake in Russian state-controlled Rosneft, mirroring the original BP-Rosneft deal, the Times said.
However, under the new proposal to be discussed at a meeting on Friday, the Rosneft stake would be owned by TNK-BP, instead of BP, and BP would gain 5 billion pounds in cash, the newspaper added.
BP and Rosneft struck a deal in January to jointly develop Arctic oil and gas, and they also signed a share swap agreement.
But Russia-connected shareholders of TNK-BP said the deal violated its shareholder agreement with BP and won an injunction in a London court to put it on hold.
(Reporting by Karolina Tagaris; Editing by Bernard Orr)