Sources to British news agency Sky News during the weekend said Hayward was considering a move on Russian oil companies Bashneft and Russneft, both partially owned by Russian billionaire Vladimir Yevtushenkov's AFK Sistema conglomerate.
Hayward, the former chief executive officer at BP, and his business partner Nathaniel Rothschild raised $2.18 billion for investment venture Vallares on the London Stock Exchange in June. The venture had said it was interested in investing in oil companies in developing countries.
Allegations surfaced last week that Vallares aims to take control over Turkey's Genel Enerji, which owns oil assets in the Kurdish regions of Iraq.
Hayward left BP last year after overseeing the immediate fallout from the Deepwater Horizon oil spill in the Gulf of Mexico, one of the worst environmental disasters in the history of the energy industry.