The former Take That star, 49, would follow in the footsteps of Geri Horner aka Ginger Spice, 50, who released her version in 2001, by putting his own spin on the timeless track.
He is quoted by The Sun newspaper's Bizarre column as saying: “I want to do a cover of ‘It’s Raining Men’ but I want Radiohead to do a backing track for me.
"But they have not got back to me.
“I keep asking but nothing back. I dunno. I might ask Trent Reznor.”
News of the 'Angels' hitmaker's cover plans come ahead of his two sold-out royal gigs at Sandringham Estate in Norfolk this month for Heritage Live, where he will be reunited with his former bandmate Mark Owen.
The 51-year-old singer is the warm-up act on both nights.
Robbie previously admitted he used to want to be like Radiohead or Oasis and not mainstream pop.
The 'Rock DJ' hitmaker told the Daily Star: "I went through a pompous moment when I didn't want to have anything to do with the mainstream stuff I used to enjoy. I thought it was babyish. I wanted to be Oasis and Radiohead.
"Then I was fortunate enough to relinquish those chains and go, 'Who am I? What do I like? What do I want to be?' And, actually, who I am is Morecambe and Wise, the Two Ronnies, Bruce Forsyth, Terry Wogan - that sort of British, professional entertainer who brought so much joy to someone like me, and now I hope to bring it to others."
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