The rapper revealed on Twitter that the socialite inspired 'Perfect Bitch', a track taken from his upcoming compilation album Cruel Summer.
"I wrote the song 'Perfect Bitch' about Kim," he said.
A source told the New York Daily News that he raps "verses about his search for the perfect woman and how he has now found the perfect bitch".
Cruel Summer, which features artists from his G.O.O.D. Music label, is now expected to be released on September 4.
West debuted new material at a New York City nightclub on Friday (August 3).
"'He was dressed in black pants and a leather T-shirt. He danced and lip-synced [to his songs]," an onlooker said.
''The room looked stunned. People were standing around with jaws literally dropped.''
Listen to Kanye West's Pusha T collaboration 'New God Flow' below: