The Mail on Sunday reported BP was working over the weekend with state-controlled Rosneft
Neither newspaper cited a source for the buyout moves.
While a buyout would end a legal spat between the two sides, industry sources played down the chances of a buyout, saying the likely cost was a challenge to BP when it was selling assets to pay the $42 billion cost of the Gulf of Mexico oil spill.
TNK-BP, Russia's No.3 oil company, has a market capitalization of $50 billion and analysts said the Russian shareholders could seek over $30 billion for their stake.
Banking sources said there was no indication that either BP or Rosneft were actively interested in buying out the billionaire shareholders.
As far as I'm aware there isn't a whole load of cash being raised to buy out that 50 percent stake in TNK-BP, one senior investment banker familiar with the situation told Reuters.
If BP paid the oligarchs in shares, and also proceeded with its plan to issue a 5 percent stake to Rosneft, as part of its Arctic exploration tie-up, this would mean the Kremlin and Russian billionaires owned a quarter of the company -- an unwelcome prospect for many BP investors.
Also, BP's taking majority control of TNK-BP would be at odds with recent Russian policy on oil investment which has been to offer foreigners only minority interests in large assets.
BP suffered another setback last Friday to its efforts to partner with Rosneft
The tribunal did, however, give BP a chance to try and extend an April 14 deadline on the swap that coincides with the British oil major's annual shareholders meeting.
An injunction remains in force against the second part of a major deal announced in January, in which BP and Rosneft would team up to explore for oil on Russia's Arctic continental shelf.
The billionaire tycoons who own half of TNK-BP have so far won every round of a legal battle against the BP-Rosneft deal, arguing that it violates the right of first refusal on BP deals in Russia enshrined in TNK-BP's shareholder agreement.
Rosneft's chairman, Deputy Prime Minister Igor Sechin, has made clear he is not interested in TNK-BP joining the exploration plan, saying the company lacked the offshore expertise, global reach and liquid international listings that BP has.
The banking sources said the Russian shareholders in TNK-BP were also interested in acquiring BP assets, including its gas operations in Algeria but industry sources said such a deal would be opposed by Algiers, which competes with Russia on the European gas market.
But a source close to the Russian shareholders played down the chances of any side deals with BP until the arbitration process is complete, adding that a further round of hearings was expected in about a month.
We are focused on completing the arbitration process with BP, the source said, adding that the tribunal still had to establish whether the BP-Rosneft share swap was a strategic deal, and therefore subject to TNK-BP's shareholder agreement.
(Additional reporting by Melissa Akin, Writing by Douglas Busvine; Editing by David Cowell)