But about 11 people in all are being considered, USA media report.
Nearly half of those polled (46%) from May 11-13 said they believed the decision to dismiss Comey was motivated by how the FBI has dealt with the investigation into Russia's alleged involvement in the USA election.
Unfortunately for the press and the public it intends to serve, White House Press Secretary Sean Spicer provided no clarity.
Fox News quoted a government source as saying they were moving "quickly and expeditiously" to find a replacement, adding: "We're doing our due diligence - we are not going to cut any corners". Trump claims he asked directly the former Director of the FBI whether he is under investigation to which he categorically replied: "you are not under investigation". She also was deputy special counsel to the Senate special committee that investigated President Bill Clinton's Whitewater scandal.
He also cast doubt on White House claims that Mr Comey had lost the confidence of his staff.
The first candidate to arrive was Alice Fisher, a high-ranking Justice Department official in the George W. Bush administration.More news: US, Europe swap air security information at laptop ban talks
McCabe, who was Comey's deputy, is expected to be replaced by a candidate now being vetted by the head of the Justice Department, Attorney General Jeff Sessions, and other White House appointees. She now works at a law firm.
The NBC News/Wall Street Journal survey in recent days said just 29 percent of those surveyed say they approve of Trump's dismissal of Comey, who was in the fourth year of a 10-year term leading the Federal Bureau of Investigation, the country's top criminal investigating agency, while 38 percent disapprove.
Earlier Friday, Trump issued an apparent warning to James Comey, tweeting that he had better hope there are no "tapes" of their conversations.
In his short letter to Comey, Trump made a specific point of mentioning that he "appreciated" how the FBI told him three times he was not personally under investigation over Russian Federation.
When questioned about the statement that the director informed the president he wasn't the subject of an FBI investigation, Trump told Holt that Comey informed him over dinner. When pressed further, Comey reportedly agreed to give Trump his "honest loyalty".
Legal experts expressed concerns about the implications of Trump's tweet. A letter from the president's lawyers, Morgan, Lewis & Bockius, released on Friday, publicly set out Russian transactions reported on Mr Trump's tax returns for the first time.