REUTERS/Joshua Roberts
"General Keith Kellogg, who I have known for a long time, is very much in play for NSA - as are three others," Trump tweeted Friday morning.
Trump is searching for a new national security adviser since Mike Flynn was forced out earlier this week amid questions about contacts he had with Russian officials. His ouster came after weeks of reports of turmoil and disorganization within the council.
The man who was Trump's top choice, retired Adm. Robert Harward, turned down the position. He described it publicly as opting for more "personal time" after four-plus decades in the military, but people close to him said the perceived chaos surrounding Trump's administration played a part in his decision.
Kellogg is currently the acting national security adviser in Trump's administration. He served in the military for 36 years and was the chief operating officer for Baghdad's provisional government during the Iraq War until 2004.
Gen. David Petraeus is also said to be in the running for the position, but one report suggested he might not accept the position if it's offered because he's aware that he's not Trump's first choice.