"To me, a great advantage is he knows many of the players. And he knows them well. He does massive deals in Russia," Trump said on "Fox News Sunday."

Ties with Russia may be a selling point to Trump, but some lawmakers on both sides of the aisle see it as a major red flag.

Sen. John McCain, R-Arizona, chairman of the Senate Armed Services Committee, told Fox News on Saturday that Putin is a "thug" and while he doesn't know the nature of Tillerson's relationship with the Russian leader, it's a matter of concern.

Speaking Sunday with CBS News' "Face the Nation," McCain said the Senate would give him a "fair hearing" and noted Tillerson's ties could be "strictly commercial."

In 2013, only a year before Russia's annexation of Crimea, Putin awarded Tillerson the "Order of Friendship."

Trump's potential secretary of state choice comes even as The Washington Post reports there are renewed concerns by the CIA about Russian interference in favor of Trump in the U.S. election.

But a Kremlin spokesman says the hacking allegation "has nothing to do with reality."

Trump is also dismissive of the matter, telling Fox News the claims were "ridiculous." His incoming chief of staff, Reince Priebus, also rejected allegations of Russian hacking and interference.

"The RNC was not hacked," Priebus said on ABC News' "This Week." "But look the Russians didn't tell Hillary Clinton to ignore Wisconsin and Michigan."

Priebus went on to say that Clinton lost the election because she had bad ideas and didn't fit the electorate.

Meanwhile, another cabinet position still under speculation is energy secretary.

Former Texas Gov. Rick Perry is said to be in the running for that position, as well as Democratic Sens. Joe Manchin from West Virginia and Heidi Heitkamp from North Dakota. Dallas investor and former Republican National Finance Chairman Ray Washburne is being considered as well.

Still, with Trump having filled out many of the key positions in his cabinet, the biggest question remains about who he will choose for secretary of state.

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