Company officials also disclosed that they had urged Obama administration officials to make US sanctions consistent with European Union sanctions, which gave greater latitude to European companies to continue taking part in some Russian projects.
Exxon Mobil is seeking permission from the USA government for approval to resume drilling around the Black Sea with a Russian partner, state-owned Rosneft, according to a person familiar with the matter. Meanwhile, the head of the Exxon's operations in Russia, Glenn Waller, said last April that the company will return to its joint project with Rosneft once sanctions against Moscow are lifted.
A State Department spokesman said Tillerson has recused himself from any matters involving Exxon for two years and is not involved with any decision involving the company before any government agency.
CNBC has reached out to Exxon and the Treasury Department for comment on the Journal's report. European companies, particularly Eni, the Italian giant, could then pick up the work.
Some Republicans in Congress, as well as some European allies, are also anxious about any sign that the Trump administration might ease some of the sanctions imposed on Russian Federation.
Notably, US Secretary of State Rex Tillerson is the former CEO of Exxon. Among other things, USA companies were prohibited from transferring advanced technology used to drill offshore and in shale formations.
Exxon applied for waiver from sanctions on Russian Federation. Exxon was ordered to stop drilling in the Kara Sea off Russia's northern coast.
Exxon has been seeking US permission to drill with Rosneft in several areas banned by sanctions and renewed a push for approval in March, shortly after its most recent chief executive, Rex Tillerson, became secretary of state on February 1.
Relations between Russian Federation and the U.S. President Donald Trump have dimmed in recent times.