Some Republicans, in an attempt to protect Trump's decision to fire Comey in the midst of his investigation into Trump associates, Russia and the 2016 election, argued that his replacement will have to be someone who has unquestionable credibility with a deep background in law enforcement matters.
Democrats agree, but argue Trump's next FBI director must also have no connections to Trump politically or professionally, making it impossible for anyone to question the next director's conflict of interest.
Working in Trump's favor is the fact that his next FBI director only needs 51 votes to get through the Senate.
Giuliani, the former mayor of New York and United States Attorney for the Southern District of New York, would likely be among Trump's top choices for FBI director, given his loyalty to the President and law enforcement background.
But his vocal advocacy for Trump during the 2016 campaign and clear partisan bent would make it nearly impossible for the former New York mayor to get confirmed by the Senate, even if he only needed 51 votes.
Giuliani's record is chock full of anti-Hillary Clinton comments, too.
"When I see her, I see her in an orange jumpsuit, I'm sorry," he said days before the 2016 election. "Or at least a striped one."
Christie is in the same boat as Giuliani.
The New Jersey governor was one of the first top flight Republicans to endorse Trump during the 2016 campaign and stood by him during some of the most trying times in his presidential campaign. His loyalty was rewarded by summarily being fired from the Trump transition, in large measure because of he, as United States Attorney for the District of New Jersey, put Trump son-in-law Jared Kushner's father in jail.
But Christie has remained loyal to Trump and was appointed to lead the President's opioid and drug abuse commission earlier this year. He has a law enforcement background and would be close to Trump.
But like Giuliani, he is clearly partisan.
"Is she guilty or not guilty," the former federal prosecutor bellowed during the 2016 Republican National Convention after talking about Clinton's character and judgment. The crowd then chanted, "Lock her up," which Christie egged on.
Should Trump consider Kelly, the former commissioner of the New York City Police Department, it wouldn't be the first time the long-time New Yorker was mentioned as a possible candidate for FBI director.
The New York Times reported in 1993, after Kelly first severed as commissioner of the NYPD after the World Trade Center bombing, that the former police cadet "has been mentioned as a possible replacement" for the FBI under then-President Bill Clinton.
Kelly didn't become FBI director. That job went to Louis Freeh.
But the fact he was considered by Clinton, a Democrat, gets to one of Kelly's strongest suits: Possible bipartisan support.
Kelly held two jobs under Clinton: Undersecretary for Terrorism and Financial Intelligence at Treasury and Commissioner of the United States Customs service.
And he has deep law enforcement credentials: He served a NYPD commissioner for 13 years, longer than anyone in history.
Pistole, currently the president of Anderson University in Indiana, is another example of someone who could curry bipartisan support.
Pistole, who last served as the administrator of the Transportation Security Administration under President Barack Obama, also served as deputy director of the FBI under former president George W. Bush.
He joined the FBI in 1983, serving at the bureau for 26 years until he was confirmed as TSA head in July 2010. While at the FBI he also worked at the bureau's Executive Assistant Director for national security.
Pistole would be a more establishment pick, given his work on terrorism policy during both the Bush and Obama administrations.
Unlike other options on this list, it is unclear whether Pistole backed a presidential candidate in 2016.
The former TSA head has commented on some Trump policies, though.
After Trump planned to cut the "armed pilot" program, training that was developed after 9/11 to prepare pilots and crew for a highjacking scenario, Pistole told The Washington Post that he disagreed.
"If you were on one of the four hijacked planes on 9/11, you'd sure say it was important," he said. "To me, it's a relatively small investment for the potential for the risk-mitigation value. It's all about how much risk do you want to take on. I would advocate for a reduction in that program but not elimination."
McCabe would likely be the easiest pick, given he is currently working at the acting director of the FBI and had served as Comey's deputy since early February 2016.
He joined the FBI as a special agent in 1996 and has since worked in on a host of issues, including counterterrorism, national security and interrogation.
McCabe's biggest drawback could be his connection to Comey and the fact that he had his hands in both the FBI's investigation into Russia's role in the 2016 election and was inside the bureau during the investigation into Clinton's emails, which Trump said in a letter Tuesday led to the FBI directors dismissal.
Picking Rep. Trey Gowdy, the South Carolina Republican and former federal prosecutor, would electrify Trump's Republican base.
Almost immediately after Comey's departure went public, right-wing blogs and websites jumped at the chance to push Gowdy, who became a champion of the right when he led the committee looking into Clinton's handling of the 2012 Benghazi attack.
Several blogs even started petitions urging Trump to appoint Gowdy director of the FBI.
Gowdy was critical of Comey's decision not to prosecute Clinton over her use of a private email server, but said in the wake of his firing that the former FBI director "had a very difficult job."
Like Giuliani and Christie, it would be difficult for Trump to confirm Gowdy, given his clear partisan bent and the fact he endorsed the President during the 2016 Republican primary.