Yukos and Kvaerner's largest shareholder, Norwegian oil and gas services group Aker Maritime - which holds a 18% stake - may soon be carving up Kvaerner, local press reported.
The company, which employs 35,000 and is desperately fighting off bankruptcy, services Yukos' Yuganskneftegas oil exploration division.
Yukos has held meetings with financier Kjell Inge Roekke, who controls Aker, to discuss Kvaerner's future.
"They invited themselves to a meeting with us earlier this week," said an Aker Maritime spokesman.
Kvaerner may be split under a deal in which Aker buys Kvaerner's oil and gas division and Yukos takes engineering and construction, the Norwegian newspaper Aftenposten reported.
Kvaerner's troubles
Kvaerner is trying to refinance its debt and wants to issue up to 2bn Norwegian crowns ($228.1 million) in new shares to help stave off bankruptcy.
Over the past months, the company's chief executive has resigned, its shares were suspended on Oslo's stock exchange, and its credit rating downgraded.
Yukos has held talks with Kvaerner for the past two months over acquiring part of Kvaerner's hydrocarbon business.
During these discussions, Yukos reportedly expressed interest for more parts of Kvaerner's E&C division.
Neither Aker nor Kvaerner would comment on the unsourced report.
Yukos said on Thursday that its unit Yukos Finance had bought shares in Kvaerner, pushing its above the 10% limit at which, under Norwegian law, companies have to declare their stake.