The 'Empire State Of Mind' rapper features on a remix of M.I.A.'s 'XXXO' and the pair also performed on stage together at last year's Grammys.
M.I.A. told MTV News: "I really want to produce for him... I have got the perfect song for Jay-Z! In fact, that's the best one that I had for my album which never made it.
"[It was] the first song I was really into and the song that actually made my album go in the direction it did, [but it] never actually made the album.
"But I want to give it to [Jay-Z], because I think it suits him more. It's insane. He's never done anything like that."
She added: "I was really surprised he liked 'XXXO', actually. And I was really surprised he liked the version that's on the album, and not Blaqstarr's version, which is more... sort of urban-sounding.
"It was interesting he liked the one with the crazy synths and stuff. It's more sort of [an] electro vibe... and his verse is so great. It was good to hear him say the word 'metrosexual'."
> M.I.A. 'chooses Nas over Jay-Z'