But the pop superstar turned down the chance to record it...
MIA has revealed that she initially offered 'Sexodus', a track from her new album, to Madonna.
As well as performing together at last year's Super Bowl halftime show, during which MIA famously gave the camera the middle finger, the pair collaborated on two tracks from Madonna's 2012 album 'MDNA', 'Give Me All Your Luvin' and 'B-Day Song'.
Now MIA has revealed that 'Sexodus' could have been recorded by the pop superstar too. "I actually played that song to Madonna when I wrote it and said, 'Oh you can have this'," MIA explained in an interview with The Guardian. "She gave it back to me."
Although Madonna apparently felt 'Sexodus' was wrong to her, the track still prompted a discussion between the two artists about what you do when you have it all. "So I was like, what d'you do? And she said, 'You spend it!' And I said, no, I don't think that's the right answer."
Asked by The Guardian whether this affected her opinion of Madonna, MIA replied: "No, because Madonna is true to Madonna. She always said she was a material girl."
'Sexodus' will now appear on MIA's forthcoming album 'Matangi' as a collaboration with The Weeknd. The long-awaited album is finally due for release on November 5 and will also include the singles 'Bad Girls', 'Come Walk With Me' and 'Bring The Noize'. MIA has recently unveiled a 90-second snippet of 'Y.A.L.A.', another new song from the album.
The 'Matangi' tracklisting in full:
'Only 1 U'
'Come Walk With Me'
'Sexodus' (feat. The Weeknd)
'Double Bubble Trouble'
'Bring The Noize'
'Know It Ain't Right'