UPDATE Feb. 18 at 8:27am | Another one bites the dust...
Former CIA chief David Petraeus has dropped out of consideration for the post, according to the Wall Street Journal.
This, just days after retired Vice Adm. Bob Harward turned down president Trump's offer.
Trump is planning to continue his search through the weekend, possibly by meeting candidates at Mar-a-Lago, his Florida home and golf resort, a senior administration official told the Wall Street Journal.
“General Keith Kellogg, who I have known for a long time, is very much in play for NSA - as are three others,” Trump said on Twitter, without naming the other candidates.
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
Here is the tweet.
Watch: 3 candidates are reportedly in the running to succeed Michael Flynn as national security adviser
The Trump administration is working quickly to name a permanent replacement after national security adviser Michael Flynn resigned Monday night.
Retired Lt. Gen. Joseph Keith Kellogg was named acting national security adviser and he is considered a top candidate. Former CIA director David Petraeus and retired Navy SEAL Robert Harward are also reportedly on the short list. This position does not requite Senate confirmation.
Why Flynn resigned
Flynn resigned late Monday night, following reports that he had misled Vice President Mike Pence and other White House officials about his contacts with Russia. It turns out that discussions of sanctions may have come up during calls with the Russian ambassador during the time leading up to Trump's inauguration.
Flynn acknowledged he gave Pence "incomplete information," originally saying he had not discussed sanctions with Russia.
From left, Lt. Gen. Keith Kellogg, David Petreaus and Robert Harward are on the short list for Flynn's old gig. (Photo: MGN/CIA/USCENTCOM)
Let's start with Lt. Gen. Keith Kellogg, the acting national security adviser He had previously been the National Security Council chief of staff, advising Trump on national security and foreign policy during the campaign along with Flynn.
Before that, Kellogg served as chief operating officer of the Coalition Provisional Authority in Iraq and as an executive at CACI International, which is a contractor for defense, intelligence and homeland security agencies.
Kellogg tweeted that Flynn "is a good man," following his resignation.
David Petraeus is another name on the short list. The former CIA director was removed from his position in 2012 after it was revealed that he passed on classified information to his biographer, who had also become his mistress.
Petraeus was under consideration to become secretary of State before Trump settled on ExxonMobil CEO Rex Tillerson.
Petraeus had been a vocal critic of Hillary Clinton during the campaign, citing her mishandling of classified materials.
Then there's Robert Harward. The retired vice admiral and Navy SEAL served as deputy commander of United States Central Command when it was under the direction of General James Mattis, Trump's secretary of Defense.
He's not new to matters of national security. Harward served on the National Security Council for President George W. Bush and commissioned the National Counter Terrorism Center.
When he retired in 2013, Harward took a job as chief executive officer at Lockheed Martin in the United Arab Emirates.