In a sign that Donald Trump was zeroing in on his choice for defense secretary Saturday, a senior transition team official told Fox News the retired Marine Gen. James Mattis was a "very strong candidate" for a Cabinet post.

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The retired general was one of several people who met with Trump in New Jersey during the day on Saturday. Trump wouldn't say whether he was offering Mattis a job, saying "we'll see." But as they posed for cameras before sitting down for their meeting, Trump pointed to Mattis and called him "a great man."

Earlier, an official with the transition team confirmed the retired general was under consideration to lead the Pentagon.

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Mattis succeeded David Petraeus as commander of U.S. Central Command, which oversees all military operations in Iraq and Afghanistan. He has field commander experience in Afghanistan and both U.S. wars in Iraq, and retired in 2013.

If nominated and approved, Mattis would be the highest-ranking officer to become defense secretary in more than half a century. When asked about a rule prohibiting those who served in active duty within the past seven years, the senior official told Fox News, "There are waivers around that."

Known as "Mad Dog Mattis," the retired general was credited with a string of colorful quotes over the years, including: "Be polite, be professional, but have a plan to kill everybody you meet."

Also: "You are part of the world's most feared and trusted force. Engage your brain before you engage your weapon."

The president-elect also was considering retired Army Gen. David Petraeus to serve as defense secretary, The Wall Street Journal reported.

Trump is said to have a strong interest in having a former general run the Pentagon, with the interest in Mattis coming after retired Army General Jack Keane, citing personal reasons, withdrew his name from consideration.

The Trump team is also weighing options for pairing the general with a CEO-like figure as deputy secretary, an individual who could bring needed reform to the Pentagon's spending and management systems.

Trump also met with Mitt Romney and Chicago Cubs co-owner Todd Ricketts, among others, at the billionaire's golf club in Bedminster, N.J., during the day on Saturday.

Trump signaled a sharp rightward shift in U.S. national security policy Friday with his announcement that he would nominate Alabama Sen. Jeff Sessions as attorney general and Kansas Rep. Mike Pompeo to head the CIA. Trump also named retired Lt. Gen Michael Flynn as his national security adviser.

A former military intelligence chief, Flynn has accused the Obama administration of being too soft on terrorism and has cast Islam as a "political ideology" and driver of extremism.

Sessions and Flynn were ardent Trump supporters during the campaign, and their promotions were seen in part as a reward for their loyalty.

In 2014, Pompeo criticized Obama for "ending our interrogation program" and said intelligence officials "are not torturers, they are patriots."

Fox News' Serafin Gomez, Doug McKelway, John Roberts, James Rosen and The Associated Press contributed to this report.