Former House Speaker Newt Gingrich expressed skepticism Tuesday at reports that former Massachusetts Gov. Mitt Romney was the frontrunner to be President-elect Donald Trump's secretary of state.

"I can think of 20 other people who would be more naturally compatible with the Trump vision of foreign policy," Gingrich told Fox News' "Tucker Carlson Tonight."

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Gingrich said that Trump would have to consider whether Romney would be a secretary of state "in the John Kerry tradition" and whether the 2012 Republican presidential nominee would "represent the kind of tough-minded, America-first policies that Trump has campaigned on."

Gingrich added that his preferred choices for secretary of state over Romney included former Arizona Sen. Jon Kyl, former U.N. ambassador John Bolton, former New York City mayor Rudy Giuliani and former Hewlett-Packard CEO and Republican presidential candidate Carly Fiorina.

However, the former Speaker added that if Trump nominated Romney to be America's top diplomat, "I'm going to support him. But President-elect Trump deserves to have the team he wants."

Gingrich also addressed Trump's offer of the secretary of housing and urban development post to former primary rival Dr. Ben Carson.

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"It would be a little bit unusual because I think Dr. Carson would be more obviously the secretary of health and human services," Gingrich said. "[But] certainly Ben Carson, anything he did, he would do extraordinarily well."