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After retired Navy Vice Adm. Robert Harward said thanks, but no thanks to becoming President Donald Trump's next national security adviser, the administration is still mulling over a list of four.

Among the contenders: the current acting national security adviser, retired Army Gen. Keith Kellogg.

Trump tweeted Friday morning that Kellogg, "who I have known for a long time, is very much in play for NSA — as are three others."

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General Keith Kellogg, who I have known for a long time, is very much in play for NSA - as are three others. — Donald J. Trump (@realDonaldTrump) February 17, 2017

The president didn't name the other three, but at least one candidate being floated is former CIA Director David Petraeus, senior administration officials told NBC News.

Trump in November tweeted that he was "very impressed" by Petraeus after meeting with him. But the retired four-star general would be a potentially explosive choice after a scandal in which he pleaded guilty in 2015 to mishandling classified information.

Related: Who are Possible Replacements for Flynn as National Security Adviser?

Trump is in need of a new adviser after retired Army Lt. Gen. Michael Flynn resigned Monday over phone calls with Russia's ambassador to the United States.

Whomever he taps will be a key confidant on sensitive security issues.

Harward, a former Navy SEAL who was also on President George W. Bush's National Security Council, told The Associated Press that he turned down the position for "purely a personal reason."

If Trump does retain Kellogg as his national security adviser, he'll be picking someone with a long resume and military experience. The 72-year-old retired lieutenant general is an Army veteran who did two tours in Vietnam and earned numerous commendations, including the Bronze Star.