"In light of these unsolicited approaches and consistent with its commitment to maximizing shareholder value, and its obligations under the Shareholder Agreement, BP has notified Alfa Access Renova of its intention to pursue a potential sale," BP said in a statement.
Besides Russia, the joint venture also produces oil in Ukraine, Vietnam, Brazil and Venezuela.
RIA Novosti reported BP's 50-percent share of the joint project could be worth $35 billion.
"I think $30-35 billion price is what we are looking at, same as it was when buyout talk has circulated earlier," said Vyacheslav Bunkov, head of oil and gas at Aton investment group.
The announcement comes less than a week after TNK-BP Chief Executive Officer Mikhail Fridman announced his resignation.
The TNK-BP partnership, formed in 2003, has been a source of friction between its British and Russian interests.
In 2007, CEO Robert Dudley was accused by Russian interests of holding the company back with BP treating the joint project as if it was a subsidiary. Russian shareholders also felt there was too much British influence when making key decisions.
Dudley was forced out of his job but has since become the CEO of BP, taking the job after Tony Hayward resigned in the wake of the Gulf of Mexico oil spill that began with an oil platform explosion in April 20, 2010.