Video showed West walk into the lobby at about 9:15 a.m. local time. He was accompanied by a large entourage, but his wife Kim Kardashian West was not with him.
Trump and West emerged from the elevator together at about 9:55 a.m. local time.
When asked by reporters what they talked about, Trump said, "Just friends, this is a good man," as he pointed at West.
"We've been friends for a long time," Trump continued. "Life, we were discussing life."
As reporters asked West several questions, he stood smiling with his arms folded.
"I just want to take a picture right now," West told a reporter.
Trump and West shook hands and Trump told him, "You take care of yourself. I'll see you soon," as the two parted ways.
West previously said he didn't vote in the election, but if he had, he would have voted for Trump.
In late November, West canceled his show at The Forum just hours before he was set to take the stage.
The following day he announced the rest of his Saint Pablo Tour had also been canceled and he was admitted to UCLA Medical Center.
West, 39, was hospitalized for more than a week as associates of his said he was suffering from exhaustion and sleep deprivation.
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