Michael Cohen, an attorney for the Trump Organization, discussed a prospective real-estate deal in Moscow with Donald Trump on three occasions during the presidential campaign, Mr. Cohen said in an interview with The Wall Street Journal.

In 2015, Mr. Cohen said, he informed the then-candidate that he was working on a licensing deal for a Trump Tower in Moscow. He subsequently asked for and received Mr. Trump’s signature on a nonbinding letter of intent for the project in October 2015. And in January 2016, he said, he informed...