The New York Times and other news organizations swiftly reported that Giuliani had told Mr. Trump of his decision in late November, but that the President-Elect refused to accept the decision.
"This is not about me; it is about what is best for the country and the new administration," Giuliani said in a joint statement released by the Trump Transition.
"From the vantage point of the private sector, I look forward to helping the President-elect in any way he deems necessary and appropriate," he added.
Giuliani will remain a vice-chair of the transition effort.
With Giuliani officially not under consideration for Secretary of State, a number of names continue to be floated, including Mitt Romney, Rep. Dana Rohrabacher (R-CA), and Exxon Mobil CEO Rex Tillerson.
The idea of Mr. Trump choosing Rohrabacher has especially raised eyebrows among some Republicans on Capitol Hill; Rohrabacher added to that fire after a feisty interview this week about U.S. policy on Russia and China, in which he accused the anchor interviewing him of being biased.
Top Trump aide Kellyanne Conway also floated the name of Alan Mulally, a former CEO at Ford Motor Company as a possible pick.
Also mentioned have been Bush Administration official John Bolton and Sen. Bob Corker (R-TN).
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