FBI Director Comey testifying before a House Judiciary Committee hearing on "Oversight of the Federal Bureau of Investigation" on Capitol Hill in Washington. Thomson Reuters President Donald Trump has asked James Comey to stay on as FBI director in his administration, The New York Times reported on Tuesday.

Comey told his top agents that the president had asked him to stay in the job, The Times said.

Comey oversaw the investigation that loomed over Democratic presidential nominee Hillary Clinton for much of the 2016 campaign. The Clinton camp accused him of tilting the election in Trump's favor by releasing a letter about the renewed interest into Clinton's private email server days before Election Day.

But Comey is also overseeing an investigation into several of Trump's political associates and their reported ties to Russia, The Times noted in Tuesday's report.

President Barack Obama appointed Comey to his position in 2013. FBI directors serve 10-year terms.

Trump met with Comey in Trump Tower earlier this month for an intelligence briefing, and Trump indicated then that he wanted Comey to stay on, according to The Times. Then during a conference call last week, Comey reportedly gave the news to senior FBI employees.