Trump appeared to have a slightly different take on the meeting, saying the men "discussed life."
"We’ve been friends for a long time," Trump said, calling West a "good man."
After the meeting, West initially declined to elaborate on what was discussed: "I just want to take a picture right now," he said.
Later in the afternoon, the rapper took to Twitter to give his take on what was said.
"I wanted to meet with Trump today to discuss multicultural issues," he wrote. "These issues included bullying, supporting teachers, modernizing curriculums, and violence in Chicago."
West added, "I feel it is important to have a direct line of communication with our future President if we truly want change."
Before finishing, he posted a hashtag "2024" without further explanation.
West floated a 2020 presidential bid a year ago at an awards show, but interrupted his concert in San Jose, Calif., last month to praise Trump.
“If I would’ve voted," Kanye told the audience, "I would have voted on Trump."
“Not only did I not vote, but there were a lot of things I actually liked about Trump’s campaign," he said. "His approach was f------ genius, because it worked."
He was hospitalized a few days later in Los Angeles, an official told ABC News, with one source saying at the time the rapper had been suffering from exhaustion and sleep deprivation, and went to the hospital voluntarily and was under the consultation of his physician.
A rep for the star has not responded to a request for comment.
West is not the first celebrity to visit the president-elect at Trump Tower. Actor and activist Leonardo DiCaprio met last week with Trump to discuss environmental issues.
In addition to West, Trump today met with Vogue editor-in-chief Anna Wintour, a Trump transition official told ABC News. He also met with Microsoft co-founder Bill Gates, who said the two discussed innovation.
Trump held a meeting with TV personality Omarosa Manigault, Cleveland Pastor Darrell Scott and NFL legends Jim Brown and Ray Lewis to discuss a program to help youth caught up in gang violence.
"We couldn't have had a better meeting,” Brown said. “The graciousness, the intelligence, the reception we got was fantastic.”
ABC News' Elizabeth McLaughlin contributed to this report.