But three officials briefed on Trump's deliberations, who spoke on the condition of anonymity because of the sensitivity of the matter, said that the pick would be Tillerson barring a late shift in Trump's thinking. NBC News first reported that Trump has settled on Tillerson.
Trump spent a month deliberating over the secretary of state position and interviewed an array of candidates, including Mitt Romney, the 2012 GOP presidential nominee and one-time critic who was the face of the Republican resistance to Trump's candidacy.
The President-elect settled on Tillerson because he projects gravitas, is regarded as a skillful manager and personally knows many foreign heads of state through his dealings on behalf of the energy giant, people close to Trump said.
In an excerpt of an interview with Fox News, which will be aired in full tomorrow, Trump praised Tillerson, though did not reveal his decision.
"He's much more than a business executive; he's a world-class player," Trump said. "He knows many of the players, and he knows them well. He does massive deals in Russia - for the company, not for himself."
Tillerson's nomination would fit the pattern of other Trump appointments, installing a wealthy business leader with little experience in policymaking. But Tillerson, 64, has spent much of his career dealing with the complexities of one of the world's biggest enterprises, spanning six continents and about six dozen nations.
The company's deep ties to Russia would potentially serve Tillerson well given Trump's desire to repair relations with the Kremlin.
But Tillerson's close relationship with Vladimir Putin could also become a flashpoint during confirmation hearings, especially in light of a recent CIA assessment that Russia intervened in the 2016 election to help Trump win the presidency, rather than just to undermine confidence in the US electoral system.
"Few corporate titans are closer to Putin than Tillerson," said Jason Bordoff, founder of Columbia University's center for global energy.
During the 1990s, Tillerson oversaw an Exxon project on Russia's Sakhalin Island and developed a working relationship with Putin.
In 2011, the company signed an agreement with the state-controlled oil company, Rosneft, to work jointly on oil exploration and development in the Arctic and Siberia.
After inking the deal in New York, Tillerson and Rosneft chairman and Putin confidante Igor Sechin dined on caviar at the luxury Manhattan restaurant Per Se, according to one account. The next day they gave oil analysts black pens with the date of the agreement engraved in gold.
Two years later, the Kremlin awarded Tillerson the Order of Friendship, honouring foreigners.
"I don't know the man much at all, but let's put it this way: If you received an award from the Kremlin, [an] order of friendship, then we're gonna have some talkin'," Graham said. "We'll have some questions. I don't want to prejudge the guy but that's a bit unnerving."
Exxon discovered oil in a well it drilled in the Kara Sea, but the joint partnership was put on ice after Russian intervention in Ukraine and annexation of the Crimea led to international economic sanctions.
As secretary of state, Tillerson, who has been critical of the sanctions, would be in a position to argue for an easing them, which could allow Exxon to resume operations.
"Russia is critical for Exxon," said Fadel Gheit, oil analyst for Oppenheimer & Co. "Not only for how much production it has there, but the potential growth is huge." He said once sanctions are lifted, "Exxon will go back to develop the Arctic business at a rapid pace."
As secretary of state, which takes the lead in international climate talks, the oil industry veteran could also play a role in unwinding US commitments under the recent Paris accord.
"The closest thing we have to a secretary of state outside government is the CEO of Exxon," Robert McNally, president of the consulting firm Rapidan Group and a director for energy at President George W. Bush's national security council.
Because ExxonMobil invests in huge, long-term projects, it is concerned "by nature with enduring interests, vulnerabilities, and opportunities," McNally said.
His selection ends one of the most high-profile contests for a top Cabinet post, whose losing candidates included former New York Mayor Rudy Giuliani, Romney and Senator Bob Corker.
Tillerson has spent his entire working life at ExxonMobil after earning a civil engineering degree and joining the company in 1975. His career has taken him from Oklahoma and Texas to Yemen and Russia, and as ExxonMobil's top executive he has cultivated relationships, meeting regularly with world leaders such as Putin, the Saudi oil minister, and the Emir of Qatar. He will retire with a nest egg of about US$300 million including stock options and pension benefits.
Yet Tillerson's track record - during a decade in which crude oil prices lurched from under US$30 to nearly US$150 a barrel - has been mixed.
The company has managed some of the world's biggest infrastructure projects often in forbidding locations, but it has spent heavily on share buybacks and has borrowed heavily to maintain both capital spending and dividend payments.
Wall Street analysts say it overpaid for XTO, a domestic shale gas company, and it has failed to meet the production targets Tillerson himself set. In April, Standard & Poor's downgraded the company's gold-plated triple A credit rating to double A plus, the first time Exxon had lost its triple A rating since the advent of colour television and the communists took over China.
Moreover, Tillerson's career with ExxonMobil isn't seen as an asset by environmentalists. The company has become a target of environmental groups that allege the company's scientists knew about the impact the use of fossil fuels was having on climate change, and that the company suppressed internal research rather than sharing it with investors and the public.
The New York and Massachusetts attorneys general have issued broad subpoenas to ascertain whether ExxonMobil's failure to disclose that information violated Securities and Exchange Commission requirements. ExxonMobil has fought back, persuading a Texas federal court to order that ExxonMobil could do discovery, depose the Massachusetts attorney general and search her internal emails and documents for any signs that she acted out of "bad faith".
"Covering up climate science and deceiving investors qualifies you for federal investigation, not federal office," May Boeve, executive director of the climate group 350.org said in a statement. "An oil baron as secretary of state would do enormous damage."
When Tillerson took the helm at ExxonMobil a decade ago, he was seen as moderating the company's position on climate change. Whereas his predecessor opposed any action on climate change, Tillerson said in 2009 that he favoured a carbon tax and proposed an initial price "somewhere north of US$20" a ton. And he reduced ExxonMobil's own emissions.
Under Tillerson, ExxonMobil also curtailed funding for the Competitive Enterprise Institute, whose energy and climate expert Myron Ebell played down the extent of climate change and said that no action was needed. Ebell has been the head of the Trump transition team on environmental issues.
Yet Tillerson still insisted that oil use was essential. He chaired the American Petroleum Institute, which hammered on the idea that jobs were at stake. "To say that you're addicted to oil and natural gas seems to me to say you're addicted to economic growth," he once told Fortune magazine.
Exxon has important relationships with countries other than Russia, most notably the Middle East. It relies on Saudi Arabia for oil supplies and is a partner in refinery projects. It has enormous liquefied natural gas export projects in Qatar. It has also managed to carry out exploration and production ventures in both Kurdistan and southern Iraq, transcending rivalries between Baghdad and the Kurds.
But under Tillerson, Exxon has also walked away from some countries. It left Venezuela after contract disputes with the late Venezuelan leader Hugo Chavez and it ended its onshore operations in Nigeria, where local insurgents sabotaged infrastructure.
Tillerson said later that "you have to be willing to say 'no, we aren't going to do it that way...if we can't do it this way, we won't be here.'"
Within the oil industry, ExxonMobil has been regarded as the most button-downed company, conservative and sometimes arrogant.
"Rex is a very, very, very honorable man," said Gheit, who is also one of his critics. "He is smart, level headed. He has tremendous resolve and very strong character."
Tillerson was born in Wichita Falls, Texas, the son of a Boy Scout administrator. He still lists the rank of Eagle Scout on his resume, and he has remained active in the organisation throughout his life. In 2012, he was instrumental in pushing the Boy Scouts board to admit openly gay youths.
The Exxon chief also chaired the US$50 million campaign to restore Washington's Fords Theatre, where President Lincoln was assassinated. ExxonMobil and Qatar were major donors.
In confirmation hearings, Tillerson can also expect to face tough questions about his views on international pipelines such as the Keystone XL, which require State Department approval. He'll also be quizzed on climate change.
"I'd expect the State Department's climate change envoy - a key role under [Hillary] Clinton and [John] Kerry - to have a lot of free time on his or her hands, and that State Department permits to build oil pipelines to Canada will be quite a bit easier to get," Bordoff said.
Tillerson has acknowledged that climate change is caused by humans, but questioned the costs of weaning the world from fossil fuels.
"What good is it to save the planet if humanity suffers," he said at a 2013 stockholders meeting, citing the outsized impact on poor people if environmental activists succeeded in establishing company goals to reduce emissions.
