Cohen recalled the conversation as well as several other racist remarks made by the president before the 2016 elections in an interview with Vanity Fair published Friday.
On another occasion, in the late 2000s, Cohen said Trump criticised African-Americans for living in "a rougher neighbourhood" in Chicago.
To recap, Cohen claimed that Trump made a number of shocking racist statements in private over the years, including "black people are too stupid to vote for me".
The ex-aide claimed that in response, Trump said "that's because black people are too stupid to vote for me".
In one example, Cohen recalls telling Trump ahead of the 2016 election that the crowd at one of his rallies was nearly entirely white.
The most-stunning admission he made in court before US District Judge William Pauley was that in 2016, Cohen had made payments of $280,000 (Rs 1.95 crore) to silence two women, who otherwise planned to speak publicly about their alleged affairs with a presidential candidate, thereby "intending to influence the 2016 presidential election".
The conversation wended its way back to the show's first season, which ended in a head-to-head between two contestants, Bill Rancic and Kwame Jackson. "He said, 'There's no way I can let this black f-g win'".
"I told Trump that [a] rally looked vanilla on television". "Why all the people from dirty holes come to the United States?", - surprised trump. "He had many African-American friends".
Former White House communications staffer Omarosa Manigault Newman, who was sacked from her job last December, claimed in her book "Unhinged" that Trump had used a racial slur on the set of "The Apprentice".
Cohen's sentencing is scheduled for December 12.
Cohen, 51, pleaded guilty in the Southern District of NY to charges of tax evasion, making false statements to a federally-insured bank, and campaign finance violations.
"I should have been a bigger person, and I should have left", he told the outlet, adding that he was in awe of the job and forgave Trump.