President Trump said he interviewed four candidates Monday in his search for his next Supreme Court nominee, as two federal appeals court judges emerged in a report as the leading contenders for the nomination.

“During the morning, I interviewed and met with four potential justices of our great Supreme Court,” he said. “They are outstanding people and they are really incredible people in so many different ways.”

Mr. Trump told reporters at the White House he plans to meet with two or three more candidates as he seeks a replacement for the retiring Justice Anthony Kennedy. He will make the announcement next Monday.

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CBS News reported that Judges Amy Coney Barrett, 46, and Brett Kavanaugh, 53, are at the top of the president’s list of 25 possible nominees. The White House had no immediate comment on the report.

Mr. Trump said last weekend that he narrowed his choice to about five candidates, including two women. He will make his announcement on July 9.