The 48-year-old rap star has ridiculed Kanye for his support of US President Donald Trump and for wearing his 'Make America Great Again' cap in his verse on 'What's Free', a new song that features on Meek Mill's album 'Championships'.
Jay - who is married to pop star Beyonce - raps: ''No red hat, don't Michael and Prince me and Ye / They separate you when you got Michael and Prince's DNA, uh / I ain't one of these house n***** you bought / My house like a resort, my house bigger than yours.''
Then, Jay - who has kids Blue Ivy, six, and 17-month-old twins Rumi and Sir with Beyonce - seemingly compared his wife to Kanye's spouse, reality TV star Kim Kardashian West.
He raps: ''My spou... (C'mon man). My route better, of course.''
Jay and Kanye, 41, have had a turbulent relationship for a number of years, even though they collaborated on the 'Watch the Throne' album in 2011.
And, speaking earlier this year, Jay admitted they were taking a break from each other.
He said during an interview with David Letterman: ''That's my brother.
''We're beyond friends. Really, like literally, my little brother is Kanye, and like your little brother, things happen sometimes ... Do you have siblings? You guys ever have a falling out? It's like that. That's your sibling forever.
''We don't come from the same mom and dad, but I watched Kanye without an album. The thing I respect about him is he is the same person who interrupted our studio session, stood on the table and started rapping. We were like, 'Could you please get down?' He was like, 'No! I am the saviour of Chicago!' He didn't even have a record.''
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