By Eric Bradner, CNN
WASHINGTON — Donald Trump is now considering more than four people for secretary of state, senior adviser Kellyanne Conway said Sunday.
"It is true that he's broadened the search and secretary of state is an incredibly important position for any president to fill," Conway told reporters Sunday morning in the Trump Tower lobby.
"He continues to talk to different people. I think you've all seen the list of four that already existed," Conway said. "This week we'll have additional interviews with other candidates for secretary of state and other cabinet positions and deputy cabinet positions as well."
Conway wouldn't reveal the names of the contenders for secretary of state, saying, "I don't think we've released that."
"That list is expanding because there is not a finite list of finalists only because he will interview with additional candidates early this week," she said.
Trump had previously tweeted that there were four finalists for the job.
But asked Sunday whether there are now more in the mix, Conway said: "More than four but I -- who knows how many finalists there will be. It's a big decision and nobody should rush through it."
A transition source said former Utah Gov. Jon Huntsman, a Republican who was President Barack Obama's first ambassador to China and ran a failed campaign for the 2012 GOP nomination, is among the candidates.
On Fox and Friends, Huntsman Jr. defended the president elect’s phone conversation with the president of Taiwan.
“Having lived in Taiwan twice and having lived in China once, there’s a little too much hyperventilating about this one,” said Huntsman Jr.
China views Taiwan as part of its territory and under the rule of its government in Beijing. The U.S. has traditionally recognized that view and avoided direct diplomatic relations with the government elected in Taiwan. Huntsman, who has lived in Taiwan twice, noted the call may be an opportunity to review the relationship with China and open up our view on Taiwan.
“If that kind of comes out of this whole discussion that people recognize that Taiwan maybe a little different than they thought. Then maybe that should create a template for the way the new Trump administration sees the region,” he said.
Monday morning Huntsman spoke at the ‘No Label’ 1787 conference in Washington D.C. He did not address rumors that he is on the short list for Secretary of State, but did take a tone similar to the president elect’s comparing the current political climate to business.
“It’s neither right, neither left, it’s where the deals get done. It’s where business is transacted. I can tell you that at the state level as Governor, that’s certainly where we got all our work done,” said Hunstman.
Vice President-elect Mike Pence wouldn't say who Trump is likely to select for secretary of state in an interview on NBC's "Meet the Press."
But he listed five men when asked about the job: 2012 GOP nominee Mitt Romney, former New York City Mayor Rudy Giuliani, former Gen. David Petraeus, Senate Foreign Relations Committee Chairman Bob Corker and former UN Ambassador John Bolton.
Asked whether Petraeus' conviction for mishandling classified information would disqualify him, Pence said: "It'll be the president-elect's decision about the totality of General Petraeus's experience in background. But I first met General Petraeus when he was commanding 101st Airborne in Iraq, and then I saw him martial the plan and the resources for what became the successful surge in Iraq. He's an American hero and he has our great respect."
CNN's Leah Freeman and Jim Acosta contributed to this report.