Donald Trump Says Exxon's Rex Tillerson Would Be ‘World-Class Player' as Secretary of State

"He's more than a business executive,'' Mr. Trump told Fox News in an interview broadcast Sunday. "He's in charge of, I guess, the largest company in the world."

Mr. Trump called it "a great advantage" that Mr. Tillerson already knows "many of the players," noting that he does "massive deals in Russia."

Those deals would be certain to come under scrutiny in Senate confirmation hearings. A number of Republicans have urged Mr. Trump to be wary of Russia, warning that it is trying to expand its influence in ways that run counter to U.S. interests in places such as Ukraine and Syria.

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Since Mr. Trump began vetting candidates for secretary of state, Mr. Tillerson's stock has climbed steadily. He moved ahead of better-known hopefuls with established political credentials--including 2012 Republican presidential nominee Mitt Romney--who had multiple conversations with Mr. Trump about the job. Mr. Tillerson is viewed by some of Mr. Trump's advisers as a mold-breaking pick who would bring an executive's experience to the diplomatic role, said a person involved in the process.

Mr. Trump said in a statement on Friday that former New York Mayor Rudy Giuliani had taken himself out of the running for the diplomatic job and other administration posts late last month.

With Mr. Trump's decision not yet final, other candidates who remain in the running, apart from Mr. Romney, are former CIA director David Petraeus, former U.S. Ambassador to the United Nations John Bolton, and U.S. Sen. Bob Corker (R., Tenn.), people familiar with the matter said.

If Mr. Trump selects Mr. Tillerson, it would add a seasoned business executive to a team that already includes three retired generals. As Exxon's CEO since 2006, Mr. Tillerson could leverage existing relationships with numerous world leaders.

Exxon has a large global presence, and this could introduce potential conflicts if Mr. Tillerson is selected. The company explores for oil and gas on six of the world's continents and has operations in more than 50 countries.

Mr. Tillerson is slated to retire next year and has retirement funds worth tens of millions of dollars, a value that could potentially be affected by State Department activities. For example, he could benefit from such potential department actions as the lifting of sanctions on Russia.