"General Keith Kellogg, who I have known for a long time, is very much in play for NSA - as are three others," Trump tweeted.
Kellogg has been named as the acting national security advisor following the resignation of predecessor Michael Flynn on Monday.
Also, Trump's tweet comes as Robert S. Harward, the retired vice admiral and former Navy SEAL who was President's top choice as national security advisor, turned down the post citing family and financial considerations.
Harward's withdrawal from consideration prompted David H. Petraeus, the former general and director of the Central Intelligence Agency, to step up his lobbying for the post, according to some reports.
Kellogg, 72, spent more than three decades in the military, serving in the Army in Vietnam and Cambodia, and then as chief of staff for the 82nd Airborne Division. He also served in the Iraqi provisional government in 2004. Kellogg was named as foreign policy advisor to Trump during the 2016 Republican primary campaign, and in December was appointed as chief of staff for the National Security Council.
Meanwhile, in another tweet President Trump praised Talk show host Rush Limbaugh for praising Friday press conference that was slammed by many.
"Thank you for all of the nice statements on the Press Conference yesterday. Rush Limbaugh said one of greatest ever. Fake media not happy!," he tweeted. (ANI)