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(CNN) —  

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.

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.