Trump is likely to announce Mattis' nomination early next week, The Washington Post reported, citing people familiar with the decision.
Mattis declined to comment, and spokespeople for Trump's transition team did not respond to the Washington Post.
Meanwhile, Trump transition spokesman Jason Miller tweeted that "no decision has been made yet" with regard to the position.
No decision has been made yet with regard to Secretary of Defense. #TrumpTransition
— Jason Miller (@JasonMillerinDC) December 1, 2016
The Washington Post noted in its report that Mattis would not be able to take the position unless Congress passes legislation to bypass a federal law stating that a secretary of defense cannot have been on active military duty in the seven years prior to their appointment. Congress has only granted this exception once in the past, when Gen. George C. Marshall served as President Harry Truman’s defense secretary.