Arizona Sen. John McCain said Saturday he is concerned about the relationship President-elect Trump's anticipated pick for secretary of state may have with Russian President Vladimir Putin.

Trump is reportedly planning to tap Exxon Mobil CEO Rex Tillerson for the top diplomatic post in his administration, a move that is likely to amplify criticisms from those who have questioned the incoming Republican president's ties to the Russian government. Putin awarded Tillerson the Order of Friendship in 2013 and his oil company has extensive business dealings with Russia.

"I don't know what Mr. Tillerson's relationship with Vladimir Putin was but, I'll tell you, it is a matter of concern to me," McCain, who chairs the Senate Armed Services Committee, told Fox News.

The Arizona Republican said he would "have to examine" Tillerson more closely before offering a firm opinion on the possibility of him serving as head of the State Department.

"You want to give the President of the United State 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," he said, adding that the U.S. cannot "have an accommodation with the Russians until they understand what Ronald Reagan taught them and that is 'peace through strength.'"

"Right now we have no peace and we have no strength," McCain told Fox.

NBC News reported Saturday that Tillerson is likely to be named secretary of state and former U.N. Ambassador John Bolton his deputy secretary. However, Trump told Fox News' Chris Wallace during a taping late Saturday afternoon that he has not yet made a concrete decision on who he will tap for the coveted Cabinet post.