The 64-year-old veteran oil executive has no government or diplomatic experience, although he has ties to Russian President Vladimir Putin. The pick would put to rest weeks-long speculation of who would earn the post as the US's top diplomat, and would place Tillerson fourth in line to the presidency.
He will also be paired with former UN Ambassador John Bolton as his deputy secretary of state, one of the sources added, with Bolton handling day-to-day management of the department.
The sources cautioned that nothing is final until the president-elect officially announces it, which could happen as early as next week.
Tillerson, who was once dubbed "T.Rex" by Sarah Palin, met Saturday with Trump at Trump Tower in New York City, the president-elect's spokesperson confirmed.
In a pre-taped interview set to air Sunday, Trump discussed why a businessman such as Tillerson would be a good fit as America's chief diplomat.
"Well, in his case, he's much more than a business executive, I mean he's a world-class player," Trump said, acknowledging Tillerson's relationship with Russia through his business dealings.
"To me, a great advantage is he knows many of the players, and he knows them well," Trump added. "He does massive deals in Russia. He does massive deals for the company — not for himself, for the company."
Trump spokesman Jason Miller said no official announcement on the secretary of state pick is expected until "next week at the earliest."