Story highlights At one point, former Sen. Joe Lieberman was considered a leading candidate

Trump has since decided he wants to see a broader range of candidates for the job

(CNN) The team tasked by the White House with finding a new director for the FBI is resetting its search, a senior administration official told CNN, after a wide range of dissatisfaction with talk of Sen. Joe Lieberman as a possible nominee.

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 Russia and was fired earlier this month. The circumstances surrounding the firing have attracted broad attention, with senators calling for an unimpeachable, nonpartisan appointment to the position designed to be a 10-year term.

At one point, Lieberman, the former Democratic senator and vice presidential nominee, was considered a leading candidate. But Trump has since decided he wants to see a broader range of candidates for the job, the official said.

The White House was not realistic in thinking it could finish the selection process before Trump left on his multi-country trip, a Justice Department source said. President Barack Obama kept Robert Mueller in the job for two additional years before settling on Comey, the source noted.

Another source familiar with the selection process said FBI officials who were concerned about the quick pace are encouraged by the reset and hope it means there won't be a rush to make the final appointment. That person, the source said, should be someone who knows the inner-workings of either the Justice Department or the FBI and also has the energy and vitality to handle the demands of the job for what is supposed to be a 10-year term.

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