Citing an unidentified senior administration official, CNN said Trump now wants to consider additional candidates for the job. Trump is also still considering former Oklahoma Gov.
President Donald Trump said last week that he was "very close" to choosing a new FBI director to replace James Comey, who was leading the investigation into possible Trump campaign ties to Russian Federation and was sacked earlier this month.
One potential complication - the Washington Post reported Tuesday that Mr. Trump hired Marc Kasowitz as his private attorney to deal with the federal investigation into Russia's interference in the 2016 USA election, and Lieberman has been working as a senior counsel at Kasowitz's law firm for several years.
After Mr. Trump's firing of FBI Director James Comey sparked controversy, the White House is seeking to allay concerns on both sides of the aisle by picking a replacement who would receive bipartisan support in the Senate.More news: Ex-CIA chief says he warned Russian Federation to stay out of election
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Even before Kasowitz was named as an expected attorney for Trump, Lieberman faced problems with Democrats as a former politician who did not have law enforcement experience, as many Democrats have called for a career-FBI official to be the next Federal Bureau of Investigation director.
The Arizona Republican said Senate Democrats were being cynical when they raised opposition to Lieberman - a close friend of McCain's - after Trump administration officials last week suggested he was one of the front-runners. "This is their nominee for vice president of the United States". Lieberman's 2006 party switch also angered many Democrats on Capitol Hill.
New US Ambassador to Israel David Friedman seen at a ceremony for new ambassadors at the President's Residence in Jerusalem on May 16, 2017.
Since then, Lieberman has gravitated back toward the Democratic fold, campaigning among Florida's Jews past year for Clinton. He still maintains ties with Republicans, however, this year testifying on behalf of two Trump nominees in confirmation hearings: Betsy DeVos, the education secretary, and David Friedman, the USA ambassador to Israel, who is the "Friedman" in the legal firm representing Trump.