From what I can tell, Sting didn't start making literary/intellectual references in his music until the 1980 album Zenyatta Mondatta where "Don't Stand So Close to Me" referred to Lolita. He was also trying to say something with "De Do Do Do, De Da Da Da."
I was trying to make an intellectual point about how the simple can be so powerful.By the album Ghost in the Machine in 1981 (the title itself refers to a book by Koestler), Sting had gone into full intellectual reference mode. "Spirits in the Material World" explores the Koestler work of the album title. "Invisible Sun" is a concept mentioned and footnoted in that book. "Secret Journey" is about a different work, called Meetings with Remarkable Men.
The album Synchronicity, of course, references Jung. There's a little shout out to Greek mythology (and geography) by mentioning the Scylla and Charybdes in "Wrapped Around Your Finger."
So, we have references to literature, mysticism, psychology, and mythology. But no Nietzsche. Maybe if the band had stayed together for one more album we would have had a release called "Übermensch" or "God is Dead." But I doubt it. I don't think that Nietzsche's inherently aggressive stance on.... well, just about anything, would appeal to Sting. If he were to explore a philosopher I would expect to see something more like the airy intellectualism of George Berkeley. If Sting releases an album called "Esse est percipi" just remember that you read it here first.