Donald Trump
Donald TrumpReuters

U.S. President-elect Donald Trump is expanding his pool of candidates for Secretary of State, The Associated Press reported on Sunday.

“There’s not a finite list of candidates” for the position, top Trump adviser Kellyanne Conway was quoted as having told reporters on Sunday. “More than four. Who knows how many finalists there will be?”

Her comments come a week after Trump’s aides confirmed that the President-elect had settled on four finalists for the post. On Sunday, however, two people close to the transition told The Associated Press that Trump is moving away from two of the four: former New York City Mayor Rudy Giuliani and Mitt Romney, the 2012 Republican presidential nominee.

That would leave former CIA Director David Petraeus as a top contender, along with Tennessee Republican Sen. Bob Corker, chairman of the Senate Foreign Relations Committee.

At the same time, the two sources told AP that Trump’s prolonged decision-making process has left the door open to other options. Among other possibilities, one official says is Jon Huntsman, a former Republican Utah governor who also served as the ambassador to China and speaks Mandarin.

The people close to the transition spoke on condition of anonymity because they were not authorized to discuss the private process publicly.

Meanwhile, a name that came up on Sunday was that of retired U.S. Navy Admiral James Stavridis, a former supreme allied commander of NATO and dean of the Fletcher School of Law and Diplomacy at Tufts University who was considered a running mate for Hillary Clinton.

A spokeswoman for Stavridis told Reuters that Trump would meet with Stavridis on Thursday, though she denied reports that Trump was interested in Stavridis as a potential secretary of state.

There was other evidence that Trump is looking beyond the known four contenders. Vice-President-elect Mike Pence on Sunday listed the quartet, but added a fresh reference to former UN ambassador “John Bolton or others who may be added to the list” of candidates.

“I think the person who will make the decision about our next secretary of state is the president-elect,” Pence was quoted as having said on ABC. “And he’ll factor the totality of Gen. Petraeus’ career in making that decision.”

Petraeus pleaded guilty last year to one misdemeanor charge of mishandling classified information relating to documents he had provided to a woman he was having a relationship with. He was spared prison time under a plea agreement with the Justice Department and was given two years’ probation.

Federal prosecutors said Petraeus knew black binders he shared with the woman contained classified information, but he nonetheless provided them.

“I made a mistake. I have again acknowledged it,” Petraeus said Sunday on ABC. “Folks will have to factor that in and determine whether that is indeed disqualifying or not.”