Cohen alleged that Trump made a disparaging comment about African-American voters when they were discussing the turnout for one of his 2016 campaign rallies.
"I told Trump that the rally looked vanilla on television. Trump responded, 'That's because black people are too stupid to vote for me,' " the President's former lawyer told the magazine.
Cohen claimed that when South African leader Nelson Mandela died, Trump remarked, "'Name one country run by a black person that's not a s***hole,' and then he added, 'Name one city.'"
He said that when he and Trump were traveling to Chicago in the late 2000s, "we were going from the airport to the hotel, and we drove through what looked like a rougher neighborhood."
"Trump made a comment to me, saying that only the blacks could live like this," Cohen told Vanity Fair.
Cohen also claimed that Trump said "there's no way'" he could let an African-American contestant from season one of "The Apprentice" be the reality show's winner.