FBI director search 'moving rapidly,' Trump says

— -- President Donald Trump said on Monday that the search for a new FBI director is "moving rapidly."

Asked how the process was going during a meeting with Abu Dhabi's Crown Prince Sheikh Mohammed bin Zayed al-Nahyan, Trump responded positively.

"Very good. It's very good," he said. "Moving rapidly."

A number of candidates for the position — including Sen. John Cornyn, R-Texas, and acting FBI Director Andrew McCabe — interviewed for the job with Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein over the weekend.

ABC News has learned of at least nine other individuals under consideration, including Rep. Trey Gowdy, R-S.C.; former House Intelligence Committee Chairman Mike Rogers, R-Mich.; and former New York City Police Commissioner Ray Kelly.

Trump plans to meet with the finalists, according to a senior White House official. Press secretary Sean Spicer confirmed that notion at Monday's White House press briefing, saying the president will conduct interviews personally after the Justice Department has made recommendations.

Spicer added that Trump is looking for "someone with high integrity and someone with the leadership skills to lead the entity."

ABC News' Katherine Faulders contributed to this report.