The singer said that he recorded the alternate rendition before Winehouse passed away in July, but decided against releasing it.
Doherty told Blag Sound: "A couple of years ago when she first released it there was an idea kicked about that I was going to do an alternate version.
"I did actually write some alternate verses and record them but in the end no-one seemed to like it so it disappeared. But I've always loved that song, it's a f**king amazing tune and I've always wanted to do some tribute."
The former Libertines star also commented on the recent riots that hit cities across the UK, saying that the modern system is "corrupt".
He said: "It was almost like a magnified version of things you see every Saturday night in Hackney, just wild kids lashing out. It was pure f**king anger.
He added: "What got me was the people getting into Ladbrokes leaping up on walls and trying to rip off the LCDs. It was insane. It's not like it's not on though.
"it's almost like the perfect reaction to the consumer society we live in. They've been asking for it. It was terrifying though."
> Pete Doherty "bewildered" by Amy Winehouse death
> Pete Doherty on prison: "It's been a rotten old few months"
Watch the full interview with Pete Doherty below: