President-elect Donald Trump has expanded his search for a secretary of state beyond the four finalists his aides previously identified, including former Massachusetts Gov. Mitt Romney, a senior adviser said Sunday.

Kellyanne Conway, who managed Trump’s election campaign, told reporters that he plans to interview additional candidates this week and does not want to rush the decision.

“It is true that he’s broadened the search, and the secretary of state is an incredibly important position for any president to fill,” she said. “He’s very fortunate to have interest among serious men and women.”

Among the other names that have surfaced for the position is Jon Huntsman, a former Republican Utah governor who also has served as ambassador to China. Huntsman sought the Republican presidential nomination in 2012, backing Romney after dropping out.

Speaking to reporters in Trump Tower, Conway declined to confirm consideration of Huntsman or to offer names of other possible contenders.

“Who knows how many finalists there will be,” she said. “It’s a big decision, and nobody should rush through it.”

Besides Romney, the secretary of state finalists whom Trump aides had previously identified were former New York mayor Rudolph W. Giuliani, a Trump confidant during the campaign; decorated military officer David H. Petraeus; and Sen. Bob Corker, R-Tenn., chairman of the Senate Foreign Relations Committee.

Trump’s consideration of Romney has been most visible, including a dinner last week in New York that Romney afterward described as “a wonderful evening.”

The choice of Romney, the 2012 Republican nominee, would send a reassuring signal to the moderate wing of the party and to the foreign policy establishment. But Trump loyalists have bristled at the prospect of rewarding someone who was among Trump’s harshest Republican critics during the campaign.

In arguing against Trump’s fitness for office, Romney called him a “phony,” a “fake” and a “con man.”

Evidence of the unease with Romney was evident at Trump’s first stop on a “thank you” tour last week in Cincinnati, where chants of “No Romney” broke out among the boisterous crowd.

Giuliani has openly campaigned for the secretary of state post but faces questions about his international business ties that could make Senate confirmation challenging.

Petraeus, a former CIA director, also has interviewed with Trump, but he has a significant liability: Last year he pleaded guilty to a misdemeanor charge of mishandling classified information, admitting that he gave sensitive materials to former lover and biographer Paula Broadwell.

During an appearance Sunday on ABC News’ “This Week,” Petraeus acknowledged his mistake and said “they’ll have to factor that in and also obviously 38 1/2 years of otherwise fairly, in some cases, unique service to our country in uniform and then at the CIA and then some four years or so in the business community.”

Corker would probably be easily confirmed by his Senate colleagues but has said he does not expect to get the job.