The 26-year-old rapper has admitted the 'Empire State of Mind' hitmaker was lined up to appear on his and Ed Sheeran's track 'Take Me Back To London' after a suggestion from the 'Shape of You' star, but Stormzy rejected the opportunity because it was "not the right song" for them to work together on.
He explains: "We were all in the studio. In my Glasto performance, there was a video [of me and Jay-Z].
"We went to the studio, we all went to make a song and the song was 'Take Me Back to London'. We were all in the studio writing, me, Ed Sheeran and Jay Z.
"Before that I loved 'Take Me Back To London' because I thought it was just going to be me and Ed and then Ed was like, 'Jay is getting on it.'
"It blew my mind. Jay-Z is my number one hero inspiration. We got into the studio and we were writing for this song and then he just stops the music and he said, 'Tell me about London, I need some inspiration.'
"Me and my manager were telling him about London and we had this powerful, beautiful, greatest conversation of my entire life so that’s where that footage [at Glastonbury] came from.
"We were talking about everything from black culture, community, music, his journey, my journey, it was the greatest conversation of my life.
"At the end he’s smiling, we were probably talking for an hour and he goes, 'So what do you think of the song?'
"I had verbal diarrhoea. I was like, 'I love this song but you being on the song changes everything.'
"'Take Me Back to London' with me and Ed is one thing, but now that Jay-Z is on it ... This is Jay-Z and Stormzy, what he means to culture, what I mean to culture ... I said, 'Is this the song?'
"I didn’t think it was the song … in my heart, in my soul musically, I just had verbal diarrhoea.
"I felt proper bad because I was like, 'You’re saying no to Jay-Z.' "
Stormzy admits Jay was "shocked" to be snubbed from the song, but he "fully understood" the reasoning behind the decision.
Speaking on Saturday night's (30.11.19) 'The Jonathan Ross Show', he adds: "I was like, 'If you didn’t ask me this, I would have just written my verse and we would have done it and I would have never questioned it but now that you’ve asked me, no.'
"I was like, 'I know how it goes, Mr Z. You are the most brilliant, busy man and I will probably never get this opportunity ever again but hand on my heart, I don’t think this is the right song for us. I don’t know why I’m saying this to you but this is not the song.'
"It is the greatest story of life. But put it this way, Jay-Z was super proud and super shocked and taken aback by the fact that this kid told him.
"He fully understood. We spoke and he made me feel [proud of what I did.] I left there thinking [I was an idiot] but then I had the honour of seeing him again and having the conversation and he let me know to my face that, what I did [was courageous] he couldn’t believe that I did it."
'The Jonathan Ross Show' airs Saturday at 10.10pm on ITV.