Geoffrey Berman.

Reports that President Donald Trump personally interviewed Geoffrey Berman, who on Jan. 5 began his tenure as interim U.S. attorney for the Southern District of New York, are “deeply disturbing” and should disqualify him as a nominee to permanently run the office, New York’s junior senator said.

In October, Politico reported that Trump interviewed Berman as well as a potential nominee for U.S. attorney for the Eastern District of New York and that the White House did not not deny that the interviews took place.

Last week, U.S. Attorney General Jeff Sessions announced that he would appoint Berman as the interim U.S. attorney in Manhattan, which carries a 120-day term.

Prior to the appointment, Berman was a shareholder at Greenberg Traurig, which also counts former New York City Mayor Rudolph Giuliani, a Trump ally, among its ranks.

Berman previously worked in the Southern District U.S. Attorney’s Office from 1990 to 1994. Last year, he donated $5,400 to Trump’s presidential campaign and has given to other Republican candidates.

At the end of the interim term, if the Senate has not confirmed Berman or another nominee for the office, the U.S. District Court for the Southern District of New York could reappoint Berman.

But in a statement, a spokeswoman for U.S. Sen. Kirsten Gillibrand said that if Trump did indeed personally interview Berman, it would be an unusual step and raises concerns about potential conflict of interest, given the fact that the Southern District U.S. Attorney’s Office would have jurisdiction over matters involving Trump.

Trump interviewing Berman would be made more disturbing by previous reports that Trump met with James Comey, the former FBI director and himself a former Southern District U.S. attorney, numerous times and reportedly asked him to pledge his loyalty, said Whitney Brennan, a spokeswoman for Gillibrand’s office.

“If this meeting took place it shows a lack of judgment that she believes her colleagues should view as disqualifying as a nominee,” Brennan said of Gillibrand.

The Southern District U.S. Attorney’s Office declined to comment on Gillibrand’s statement. U.S. Sen. Charles Schumer’s office did not respond to a request to comment, but numerous media outlets—quoting unnamed sources—said that Schumer also has concerns about appointing Berman to the post once held by Preet Bharara, who was fired last March after he refused to resign.

Berman is widely believed to be the White House’s nominee to be the full-fledged Southern District U.S. attorney, though he would be subject to the “blue slip” process, wherein the two senators from the state where a judicial nominee resides provide a thumbs up or thumbs down on a nominee for federal prosecutor.

Following Politico’s report on the interview with the potential nominees for U.S. attorney, Bharara tweeted that it is neither “normal nor advisable” for Trump to interview potential nominees, especially one for his old job.

U.S. Sen. Richard Blumenthal, a Connecticut Democrat who sits on the Senate Judiciary Committee, tweeted last week that Berman’s appointment is “absolutely abhorrent to the rule of law” and raises questions about the integrity of the federal prosecutor’s office in Manhattan.

But Robert Fiske Jr., senior counsel to Davis Polk & Wardwell who served as Southern District U.S. attorney from 1976 to 1980, said Trump has the right to interview possible appointees. He said President Gerald Ford did not interview him before his appointment as Southern District U.S. attorney but that he “wouldn’t have thought twice” about agreeing to do so.

“If something nefarious comes up in the conversation, you deal with it,” Fiske said.

On his first day on the job, Berman announced that he was hiring Robert Khuzami, a partner at Kirkland & Ellis who is himself a Southern District alum, as his deputy.

A former federal prosecutor who declined to be named said the timing of Khuzami’s hiring seems to indicate that Berman was likely coordinating with Khuzami ahead of his appointment to lead the Manhattan office, and the person said they found the timing interesting.

“It’s a little strange in the sense that it kind of presumes that you’re going to get the job—he hasn’t been nominated yet,” the person said. “You sort of hope that everything works out because it could be pretty awkward if 120 days go by and for some reason the nomination doesn’t go forward. And then what do you do if you’re Khuzami, or Berman?”

Reached by phone, Khuzami declined to comment on whether he had contact with Berman about the position prior to Berman’s interim appointment.

—B. Colby Hamilton contributed to this article.