ExxonMobil chief's stock rises in Trump secretary of state search

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Exxon boss considered for secretary of state position

President-elect Trump considers Rex Tillerson for Cabinet nomination

ExxonMobil Chairman Rex Tillerson’s stock is rising in Donald Trump’s ever-expanding search for a secretary of state nominee, according to a source close to the president-elect – though Fox News is told other big names remain in the mix.

Trump met earlier this week with Tillerson, whose company is based in dozens of countries across six continents and has had business dealings in Russia, Yemen and other hot spots. A source close to Trump said the president-elect was impressed with Tillerson, and the two men are likely to meet again in the coming days.

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Senior adviser Kellyanne Conway, speaking Friday with “Fox & Friends,” acknowledged the field has “widened,” and said the final decision will factor in whether a prospective nominee will adhere to “the Trump doctrine” and is willing to “execute on his vision.”

“You’re just talking about a very diverse group,” Conway said, without commenting on who may be the favorite at this stage. “I think this is a tremendous process, because you can’t rush through such an important selection.”

The 64-year-old Tillerson began his career at Exxon in 1975 as an engineer, rising through the ranks and becoming president and director in 2004 and CEO two years later. He was born in Wichita Falls, Texas, and studied civil engineering at University of Texas.

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Should he become America's top diplomat, he will have a pay cut and complicated financial situation to sort out. Tillerson reportedly makes more than $40 million per year and owns more than $100 million of stock in a company that has holdings and dealings throughout the world.

Conway said other names remain in the mix, including: 2012 GOP presidential nominee Mitt Romney, former New York Mayor Rudy Giuliani, Ford CEO Alan Mulally, retired Gen. David Petraeus and Sen. Bob Corker. She also mentioned former U.N. ambassador John Bolton and Rep. Dana Rohrabacher.

“I just think it’s going to come down to one man’s decision,” she said, adding that another significant factor is whether the pick can comfortably work with other Cabinet members. “It’s very important to have a cohesive Cabinet.”

Fox News was told, though, that Bolton and Rohrabacher are being considered more for deputy secretary. As for the other secretary candidates, the source close to Trump said Romney is in play but there are concerns the former Massachusetts governor’s scathing March speech opposing Trump’s candidacy would overshadow him traveling abroad to world capitals.

In that address, Romney called Trump a “phony” and a “fraud” who would make America less safe, and even questioned his business acumen.

Giuliani, meanwhile, “could have had DHS” but turned it down, the source told Fox News.

Going for Corker is that he could have an easy confirmation before his colleagues in the Senate, a point Conway cited on “Fox & Friends” Friday morning.

A Tillerson pick could represent major changes for foreign policy.

The Wall Street Journal reported that Tillerson has close ties to Russian leader Vladimir Putin and other world leaders. A Tillerson appointment also could raise complex ethical questions, the report noted, as he owns Exxon shares worth $151 million – and the company has operations in more than 50 countries.

The president-elect met with Tillerson Tuesday at Trump Tower.

While meeting with dozens of people for interviews and advice at his headquarters in Manhattan, Trump has been naming appointees at a rapid pace in recent days. He most recently has settled on his picks to lead the Labor Department, Homeland Security Department, Small Business Administration and Environmental Protection Agency.

Fox News’ Jennifer Griffin contributed to this report.