President-Elect Donald Trump announced on Friday that former New York Mayor Rudy Giuliani would not be chosen for a post in the Trump Administration, as speculation swirled on Trump’s seemingly expanded and extended search for a Secretary of State, the highest-profile job still not filled by Mr. Trump.

Giuliani, who was often by Mr. Trump’s side for months on the campaign trail, had been considered by many to be a leading candidate for a Cabinet job, but it did not pan out that way.

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).