Mitt Romney. Drew Angerer/Getty Images President-elect Donald Trump is down to his final four candidates in what has been a drama-filled search for his secretary of state.

Republican National Committee communications director Sean Spicer told reporters during a Wednesday morning press call that Trump was down to four candidates for the administration post. Spicer said no additional appointments are expected this week.

On Tuesday, Bloomberg reported that the search was down to five candidates: 2012 Republican presidential nominee Mitt Romney, Senate Foreign Relations Committee Chair Bob Corker, former CIA Director David Petraeus, former New York City Mayor Rudy Giuliani, and retired Marine Corps Gen. John Kelly. Trump is meeting with Kelly on Wednesday.

It's not clear which of the four is out of the running. Romney, Corker, and Petraeus all met recently with Trump to discuss the post. Giuliani, an early favorite, has seemingly fallen out of favor over the past few weeks.

After a high-profile dinner with Trump last night, Romney told reporters he has "increasing hope" the president-elect can lead the US to a "better future."

"What I've seen through these discussions I've had with President-elect Trump, as well as what we've seen in his speech on the night of his victory, as well as the people he's selected as part of his transition — all of those things combined give me increasing hope that President-elect Trump is the man who can lead us to that better future," Romney said.

But while Romney is viewed by many as the front-runner, some within Trump's camp, such as senior adviser Kellyanne Conway, have criticized Romney for ridiculing Trump throughout the campaign.

Corker, a Tennessee Republican, also seemed to needle Romney after a meeting the senator had with Trump on Wednesday, saying that the head of the State Department must be extremely loyal to the president.

"The secretary of state's role is so important to a president," Corker told reporters, according to a pool report. "He needs to choose someone that he's very comfortable with and he knows that there's going to be no daylight between him and them. He needs to know that the secretary of state is someone who speaks fully for the president."

Asked whether Trump told him about a timeline for the decision, Corker said they "didn't talk about that."

And following his meeting with Petraeus, who pleaded guilty in 2015 to a misdemeanor charge of mishandling classified information, Trump tweeted that he "was very impressed!"

But the idea of Petraeus as secretary of state, after Trump and fellow Republicans lambasted Democratic presidential nominee Hillary Clinton for her handling of classified information as secretary of state, has been criticized. Sen. Rand Paul of Kentucky on Wednesday said he didn't know how Senate Republicans could confirm the former CIA director "with a straight face."