FBI director search 'moving rapidly,' Trump says

Candidates include Sen. John Cornyn and former NYPD Commissioner Ray Kelly.

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."

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.