Censor.NET reports referring to The Sunday Times citing sources close to the American president-elect.
"Tillerson's appointment, if confirmed, will fuel concerns about the extent of the incoming Trump administration's links with the Kremlin. In 2011, Exxon Mobil signed a deal with Rosneft, Russia's largest state-owned oil company, for joint oil exploration and production.
"Since then, the two companies have formed 10 joint ventures for projects in Russia. In 2013, Putin, whom Tillerson has known for more than two decades, bestowed on him his country's Order of Friendship," the article notes.
"Sources close to Trump said that Tillerson had been picked for the job after an exhaustive interview process. Other candidates considered included Mitt Romney, the defeated 2012 Republican presidential nominee, whom Trump met twice, and Rudolph Giuliani, the former mayor of New York," the publication reads.
Congressman Dana Rohrabacher of California, who once arm-wrestled Putin in a Washington bar when he was mayor of St Petersburg, is under consideration to be ambassador to Moscow, U.S. officials told The Sunday Times.
As noted, the report of Tillerson's expected advancement came as the president-elect angrily denounced a CIA assessment that Russia hacking had been aimed at helping him defeat Hillary Clinton in last month's presidential election.
Further on, Trump's refusal to accept that Russia engaged in hacking activities and his pointed barb about Iraq intelligence failures could pitch him into open war with the CIA, even as it briefs him weekly about covert operations.