Rosneft has valued the venture at $50bn, and BP’s share of it at approximately half that.
The Russian company also made a buy offer earlier this week to BP’s partners in the venture, the AAR consortium owned by four Soviet-born billionaires.
The deal could leave BP and the AAR consortium with lump sums of cash, and minority stakes in Rosneft, which already dominates the increasingly state-owned Russian oil industry.
BP’s board is expected to discuss the deal today, which would make Rosneft the largest listed oil producer in the world.
In June BP said it planned to sell its profitable stake in the venture, due to relationship problems with their Russian partners.
Relationships were strained last year when BP attempted to form an exploration alliance with Rosneft.
AAR was unhappy with this, and secured a High Court injunction to block the plan.
Since 2003 BP has invested $8bn into the TNK-BP venture, and has seen dividends of about $19bn.
The venture accounts for roughly 10 percent of BP’s profits.