This comes after Spicer, Sanders, Vice President Mike Pence and Trump gave conflicting reports for why former FBI Director James Comey was sacked earlier in the week.
Trump's administration - embroiled in a deepening crisis over the sacking and its shifting explanation of events - is interviewing the first candidates for the post on Saturday, US media reported.
"We can make a fast decision", Trump told reporters aboard Air Force One before flying to Lynchburg, Virginia, to deliver a commencement address at Liberty University. He later said he was "not aware" whether any White House official had recordings of the conversation and wouldn't comment on whether the president regularly recorded conversations in the Oval Office.
Reuters White House Correspondent Jeff Mason first asked, "Did President Trump record his conversations with former FBI Director Comey?"
"I don't think it's inappropriate", Trump said.
Mr Trump said the candidates were "outstanding people" and "very well known".
Mr. Trump has said that Mr. Comey told him three times-once at a dinner and twice over the phone-that he wasn't under investigation.
Antonio Conte Insists He's Staying At Chelsea
We have the possibility to win the title without the wait for the Tottenham result. We know West Brom are a hard team to play against.
- Who are the candidates?
The White House has said Comey's firing was unrelated to the Russian Federation probe, but in the interview with NBC News on Thursday, Trump said he knew he ran the risk that by firing Comey he would "confuse people" and "lengthen out the investigation" into ties to Russian Federation.
The 49-year-old McCabe, a career FBI agent, has taken part in a number of high-profile investigations, including probes into the Boston Marathon bombing in 2013 and the attacks against USA installations in Benghazi, Libya in 2012.
Critics have assailed Trump for firing the Federal Bureau of Investigation chief at a time when the agency is investigating alleged Russian meddling in the 2016 USA election, and possible collusion between Moscow and the Trump presidential campaign. John Cornyn of Texas, the No. 2 Senate leader and a former state attorney general.
Fisher formerly served as assistant attorney general for the Justice Department's Criminal Division. Other possibilities being considered apparently include former Justice Department lawyer J. Michael Luttig, Republican congressman Trey Gowdy of Benghazi-investigation fame, and former Republican congressmember (and former FBI agent) Mike Rogers, who once chaired the House Intelligence Committee.
The day after acting FBI Director Andrew McCabe contradicted a number of the Trump administration's talking points about James Comey's firing during sworn testimony, White House Press Secretary Sean Spicer refused to confirm whether Trump has confidence in McCabe. Comey had come under intense scrutiny for his role in the FBI's investigation into the email practices of Trump's opponent, Democrat Hillary Clinton, and the reopening of the investigation just days before the election.
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