BP is conducting secret, high-level talks with its Russian billionaire partners in TNK-BP and an outline deal to settle their dispute may come in weeks, a source familiar with the matter said.

Lamar McKay, a top BP troubleshooter brought in to resolve a long-running dispute over strategy and management control at TNK-BP, held a five-hour meeting in London the week before last with Mikhail Fridman, the billionaire oligarch who calls the shots among the Russian shareholders, the source added.

"The initial idea was to negotiate a quick two-pager to cease hostilities but this has now turned into something more substantial around agreeing the principles of how to run the company," the source said, speaking on condition of anonymity. "A deal is a few weeks away. They are likely to sign something."

Stan Polovets, CEO of the billionaire's AAR consortium, declined to discuss the talks. "We agreed not to comment on the negotiations, and we feel it's really important to honor that agreement," he said.

A BP spokesman in Russia also declined to comment, beyond confirming that general talks were going on.

The source said talks were based on the idea that both sides would keep their 50-50 stakes but that any deal would probably give the oligarchs more say in how the company is run. One of the toughest issues in the talks is who would replace CEO Robert Dudley, the source said.