During Wednesday's episode of "Jimmy Kimmel Live," the two quickly dispelled the idea that their feud was a publicity stunt, saying their beef was authentic.
They discussed why West often comes off as arrogant.
"I don't know if you know this, but a lot of people think you're a jerk," Kimmel said after West called himself a genius. West was objecting to the idea that he's "just a celebrity."
"When you said you think you're a genius, I think that upsets people," Kimmel said. "But the truth is a lot of people think they're geniuses, but nobody says it because it's weird to say it. But it is most certainly more honest to say, 'I am a genius.'"
The feud started in late September when the nightly hour-long show aired a skit that mocked West's radio interview by having a child re-create it. In the BBC Radio 1 interview, West declared himself the "biggest" rockstar in the world.
"Does Kanye West know he's not supposed to be his own hype man?" Kimmel asked before showing a clip of the interview.
The musician responded with a series of Twitter messages that labeled the comedian out of line and unfunny.
"Jimmy Kimmel is out of line to try and spoof in any way the first piece of honest media in years," West wrote on Twitter.
The Associated Press contributed to this report.