The White House has said Mr. Trump could name a new director as soon as Friday before he leaves for his first trip abroad with stops in the Middle East and Europe.
Mr. Trump made the remarks during a press photo spray as he met with Colombia President Juan Manuel Santos in the Oval Office.
Asked whether Mr. Lieberman, a former senator from Connecticut and the 2000 Democratic nominee for vice president, was still among the finalists, Mr. Trump gave an emphatic “yes.”
Senate Democrats said earlier that they wouldn’t accept anyone with a political background, which seemed to eliminate Mr. Lieberman.
It also would rule out for Democrats another finalist, former Oklahoma Gov. Frank Keating, a Republican.
Mr. Trump has moved quickly to fill the job since firing James B. Comey last week, which ignited a firestorm of criticism in Washington and new charges that he was interfering with the FBI’s Russia investigation.
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