President-elect Donald Trump is expected to nominate ExxonMobil CEO Rex Tillerson for secretary of state on Tuesday morning after former Massachusetts Governor Mitt Romney ruled himself out.

Trump, who teased an announcement on Monday night, met with Tillerson twice during the past week and pointed to the CEO's deep relations with Moscow as a selling point during an interview with Fox News on Sunday.

As ExxonMobil's head, Tillerson maintained close ties with Russia and was awarded the Order of Friendship by President Vladimir Putin - a sticking point among several Republican senators who find his cozy relationship troublesome.

After the initial favorite, former New York Mayor Rudy Giuliani withdrew himself from consideration, Tillerson emerged as a frontrunner several weeks into the deliberation.

Romney and other contenders such as former CIA director David Petraeus and Republican Senator Bob Corker of Tennessee, all received calls on Monday informing them of Trump's decision to nominate Tillerson, the New York Times reported.

Romney shared a statement on his Facebook that read: 'It was an honor to have been considered for Secretary of State of our great country. My discussions with President-elect Trump have been both enjoyable and enlightening.

'I have very high hopes that the new administration will lead the nation to greater strength, prosperity and peace,' he added.

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Trump (left) is expected to nominate ExxonMobil CEO Rex Tillerson (right) as the US secretary of state after they met twice during the past week

Trump revealed his plans on Monday night. He praised Tillerson on Sunday and told his Twitter follower to 'stay tuned'

Trump reportedly called Romney to break the news that he was not selected

Romney then ruled himself out of the running, saying it was an 'honor to be considered'

Romney, the 2012 Republican presidential candidate, was a vocal critic of Trump, although the two appeared to make up as the president-elect considered him to head the State Department.

But some of Trump's senior advisers warned that tapping Romney for the job would anger the president-elect's loyal supporters.

Trump was not familiar with Tillerson until he was recommended by former defense secretary Robert Gates and James Baker III, who worked as secretary of state under George H. W. Bush, the Times reported.

Both Trump's son-in-law Jared Kushner, and his chief strategist Stephen Bannon backed Tillerson, who hit it off with Trump, according to the Times.

NBC News first reported Tillerson would be chosen as secretary of state, citing two sources close to the transition team. Fox News also reported the ExxonMobil executive as Trump's pick on Monday.

The president-elect praised Tillerson during a Fox News interview that aired Sunday, saying: 'He’s more than a business executive – he’s a world-class player.'

He added that it was ‘a great advantage’ that Tillerson knew ‘many of the players’, and did ‘massive deals in Russia’.

Russia's Prime Minister Vladimir Putin speaks with Rex Tillerson in Sochi in 2011

In 2011, ExxonMobil signed a deal with Rosneft, Russia's largest state-owned oil company, for joint oil exploration and production. Since then, the companies have formed 10 joint ventures for projects in Russia.

In 2013, Russian President Vladimir Putin awarded Tillerson his nation's Order of Friendship.

But the energy deal was put on hold when the US and European allies imposed sanctions against Russia for annexing Crimea.

ExxonMobil reportedly vowed to resume the agreement once sanctions were lifted – and Tillerson has already spoken out against trade penalties on Russia, claiming they harm ordinary people in the country.

Tillerson, who is expected to retire from ExxonMobil next year, also has tens of millions of dollars of his pension tied to the oil firm, presenting possible conflicts of interest.

Supporters, however, claim he is a skilled negotiator who has vital experience dealing with world leaders.

'He has had more interactive time with Vladimir Putin than probably any other American with the exception of Henry Kissinger,' John Hamre, a deputy defense secretary to Bill Clinton told the Wall Street Journal.

Tillerson emerged on Friday as Trump's leading candidate after former New York Mayor Rudy Giuliani (left) formally withdrew from consideration for secretary of state

Romney and other contenders received calls on Monday informing them of Trump's decision to nominate Tillerson. Pictured, Romney and Trump having dinner in New York in November

Tillerson's close ties to the Kremlin, however, is a worrisome sign to many, especially after the CIA's conclusion that Russia interfered in the US elections with the goal of seeing Trump in the White House.

Republican Senator John McCain, along with majority leader Mitch McConnell, have voiced their support for a congressional investigation into Russia's involvement.

McCain also told Fox News that Tillerson's links to Putin were a 'matter of concern to me.'

'You want to give the president of the United States the benefit of the doubt because the people have spoken. But Vladi­mir Putin is a thug, a bully and a murderer, and anybody else who describes him as anything else is lying,' McCain said.

Senator Marco Rubio also tweeted his displeasure about the potential pick on Sunday.

'Being a 'friend of Vladimir' is not an attribute I am hoping for from a #SecretaryOfState,' Rubio wrote, initialing the tweet to ensure Americans knew it was coming directly from the senator's mouth.

If Tillerson is nominated, climate change could be another divisive issue. ExxonMobile is under investigation by the New York Attorney General's Office for allegedly misleading investors, regulators and the public on what it knew about global warming.

On Monday, Trump's senior adviser Kellyanne Conway was forced to defend Tillerson against claims he's too friendly with Russia, saying: 'It's not like he's pounding down vodka with Vladimir Putin at the local bar'.

Tillerson 'has dealt with Russia for many years,' Conway said, adding that he has dealt with Putin 'in a business context.'

'We know we don't have a good relationship with many countries around the world, including Russia,' she insisted.

'If, as secretary of state, Rex Tillerson or whomever the president-elect chooses ... if he can go ahead and improve relationships and advance American interests and advance the Trump doctrine, then we should all welcome that,' Conway added.

She noted that Tillerson 'has been at Exxon for 41 years, employs 70,000 people [and] is in charge of a $320 billion global corporation.'

Tillerson emerged as Trump's leading candidate after former New York Mayor Rudy Giuliani formally withdrew from consideration for secretary of state.