But about 11 people in all are being considered, USA media report.
As Mr Trump works to fast-track Mr Comey's successor, lawmakers from both parties urged him to steer clear of any politicians for the job and said he must "clean up the mess that he mostly created".
By Wednesday, White House officials were saying that Trump had contemplated firing Comey for a long period of time, but made the final determination after hearing from Sessions and Rosenstein.
Trump also hit back on Friday at media reports questioning the credibility of White House accounts of why Comey was sacked, which have changed over the course of the week, and threatened an end to regular White House press briefings.
Spicer repeatedly said "the president has nothing further to add on that" and eventually insisted: "The tweet speaks for itself".
Reports published Thursday, citing unnamed sources close to Comey, said Trump invited Comey to dinner and then asked Comey to promise he'd be loyal to him.
However later in the day the US House Democrats have demanded that the White House hand over to the Congress the tapes of the January dinner between US President Donald Trump and former FBI Director James Comey.
"And we think that we've actually, by removing Director Comey, taken steps to make that happen", she added.
In a letter released to the press on Friday afternoon, two top congressional Democrats, Elijah Cummings of Maryland and John Conyers of MI, asked the White House to hand over any such tapes "if they exist".
Critics have assailed Trump for abruptly dismissing Comey, who was leading the agency's investigation into alleged Russian meddling in the 2016 US election, and possible ties between Moscow and the Trump presidential campaign.
Still, Trump's comments about "tapes" - which echoed the secret Watergate recordings made by ousted former President Richard Nixon - immediately drew sharp rebukes from Capitol Hill.
Under Comey, the Federal Bureau of Investigation was in the middle of looking into Trump's connections to Russian Federation, both during the election campaign and at present.
When he came out with that scathing set of circumstances, the server... the emails, 33,000 emails... "And that's what we want for the FBI", Trump said.
He questioned whether his administration should cancel all future press briefings and, instead, replace them with written responses to questions, "for the sake of accuracy". NY state judge Michael Garcia, acting FBI Director James McCabe, Senate Majority Whip John Cornyn and the former head of the Justice Department's Criminal Division, Alice Fisher, will be interviewed by Attorney General Jeff Sessions and his deputy Rod Rosenstein.
Donald Trump has refused to deny recording his meetings with former FBI Director James Comey.