The Wall Street Journal reported Wednesday that Exxon made the request to resume a joint venture with Russian oil company PAO Rosneft.
The application asks to be exempted from U.S. sanctions against Russia so the companies can drill in various banned locations in the Black Sea.
The Journal and The New York Times cited sources close to the matter in its report. Exxon has sought drilling access to the region since late 2015.
Such a request from the Texas-based oil giant isn't surprising to many experts. U.S. Secretary of State Rex Tillerson is ExxonMobil's former chief executive.
The Treasury Department's Office of Foreign Assets Control can issue waivers to enable companies to dodge sanctions, but the matter is likely to be scrutinized in Congress and other corridors in Washington, D.C., because it comes at a time of deep distrust between the United States and the Kremlin.
The U.S. Department of State also has a say in the waiver application, the Journal reported.
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