But Priebus cautioned that it's a "little premature to be claiming" the secretary of state choice for the incoming Trump administration is a "done deal."
Tillerson has emerged as the likely pick for secretary of state, with former United Nations Ambassador John Bolton as the likely choice for deputy secretary of state, three senior Trump transition officials told ABC News this weekend.
Priebus said in an interview with ABC News' George Stephanopoulos on "This Week" that Tillerson "is an incredible businessman and American patriot and somebody I think who has experience across the globe that very few people have. I also think we’ve got other great choices to make."
"There’s no announcement that’s coming today, George, as far as secretary of state’s concerned," Priebus added. "So it’s a little premature to be claiming that this is a done deal."
"Whether I choose him or not for "State"- Rex Tillerson, the Chairman & CEO of ExxonMobil, is a world class player and dealmaker. Stay tuned!" Trump tweeted.
Senators from both sides of the aisle, including Sen. John McCain, R-Ariz., and Sen. Marco Rubio, R-Florida, have raised questions about Tillerson because of his close ties to Russia.
Rubio tweeted this morning, "Being a "friend of Vladimir" is not an attribute I am hoping for from a #SecretaryOfState - MR"
Tillerson's business relationship with Russia dates back to the 1990s, when he assumed responsibility for all of Exxon Mobil's holdings there.
In 2011, Exxon Mobil forged a deal with Russian oil company Rosneft, which, at that time, was 75 percent owned by the Russian government. The deal gave Exxon Mobil access to arctic oil deposits, and Putin attended the signing ceremony.
In 2013, the two companies expanded their partnership. That same year, Tillerson received one of Russia's highest civilian honors, the Order of Friendship, from Putin.
In 2014, after Russia annexed Crimea, Exxon was forced to halt the deal due to sanctions. Although Exxon Mobilput out a press release noting they were “winding down” their operations following the sanctions, Tillerson reportedly called them “ineffective” at his 2014 shareholders meeting.
On "This Week," Priebus said he doesn't see Tillerson's relationship with Russia and with Putin as a negative.
"The fact that he actually has a relationship with people like Vladimir Putin and others across the globe is something that shouldn't be -- we shouldn't be embarrassed by it, it's something that I think could be a huge advantage to the United States," Priebus said.