John?   No, it's Sting.

From the beginning, John Constantine has had a remarkable resemblance to the pop star Sting.  In an interview with Wizard magazine, Alan Moore clears up some of the misconceptions surrounding the creation of John Constantine, and his relationship with the rock superstar.  And he tells an interesting little story.  

Try as I might, I simply couldn't find a Rolling Stone interview in which Sting expressed any opinion on any comic, let alone Hellblazer.  However, I did find an interview in Musician magazine in which Sting briefly discusses his relationship to his comic book counterpart, which may be what Alan Moore is referring to.  
 

The Unexplored Medium
ALAN MOORE speaks on what makes working as a comic writer so appealing.

The following excerpt comes from an article which appeared in the November 1993 issue
of Wizard magazine. The authors were William A. Christensen and Mark Seifert

Where did the character John Constantine come from?

Basically, when I take over something as a writer, I always try to work as closely as I can with the artists on the book, so I immediately did my best to strike up a friendship with Steve Bissette and John Totleben. I asked them what they would like to do in Swamp Thing . They both sent me reams of material. Things that they had always wanted to do in Swamp Thing, but never thought they would get away with. I incorporated this into my scheme of things, and tried to pin it all together.

One of those early notes was they both wanted to do a character that looked like Sting. I think DC is terrified that Sting will sue them, although Sting has seen the character and commented in Rolling Stone that he thought it was great. He was very flattered to have a comic character who looked like him, but DC gets nervous about these things. They started to eradicate all traces of references in the introduction of the early Swamp Thing books to John Constantine's resemblance to Sting . But I can state categorically that the character only existed because Steve and John wanted to do a character that looked like Sting. Having been given that challenge, how could I fit Sting into Swamp Thing ? I have an idea that most of the mystics in comics are generally older people, very austere, very proper, very middle class in a lot of ways. They are not at all functional on the street. It struck me that it might be interesting for once to do an almost blue-collar warlock. Somebody who was streetwise, working class, and from a different background than the standard run of comic book mystics. Constantine started to grow out of that.

One interesting anecdote that I should point out is that one day, I was in Westminster in London -- this was after we had introduced the character -- and I was sitting in a sandwich bar. All of a sudden, up the stairs came John Constantine. He was wearing the trenchcoat, a short cut -- he looked -- no, he didn't even look exactly like Sting. He looked exactly like John Constantine. He looked at me, stared me straight in the eyes, smiled, nodded almost conspiratorially, and then just walked off around the corner to the other part of the snack bar. I sat there and thought, should I go around that corner and see if he is really there, or should I just eat my sandwich and leave? I opted for the latter; I thought it was the safest. I'm not making any claims to anything. I'm just saying that it happened. Strange little story.

The following excerpt comes from an article/interview
with Sting appeared in the August 1991
issue of Musician magazine. The author was Bill Flanagan.

Wherever Gordon Sumner ends, there's no question that the public image of Sting has taken on a life of its own. . . . Last night Sting was talking about the DC superhero comics of the early '60s when he was reminded that these days DC has a supernatural hero, Hellblazer, modeled after Sting. As a kid Sting read about Superman and Batman. Now he's in the comics hanging out with them.

"That's not me," Sting says. "That's the public domain creation. Anything can happen to that, bad or good. It doesn't affect the core of me. Having created a kind of mask or image, you should then put it aside and get on with your life. The mistake [celebrities] make is they, confuse that thing that's been created by them and by the media for reality. Then they sit inside that thing and they wonder why everything's fucked up. That character is someone else. It's not me. And thank God. Nice things happen to it, bad things happen to it - fine. Just leave me out of it!