Warner Bros has asked the director to re-edit the critically-panned epic movie, reports Collider.
The most recent version of the 2004 movie arrived on DVD in 2007.
"[I didn't go back] for money," said Stone at a Universal Pictures dinner of the previous cut, which added 40 minutes of footage.
"I just did it because I didn't feel I had finished the movie, and I felt like I was rushed... It took three years [for me] to fully understand [Alexander].
"I'm going to go back next year actually. I've been asked by Warner Brothers because they did so well with 'The Final Cut'. They actually sold more than a million copies. They've asked me to go back next year and do a fourth version.
"Frankly, it's a movie about history and I just feel like I can add something more. I wouldn't do it otherwise... I don't need more footage. I want to cut it down now because I added too much. I want it to come back a little bit."
Alexander starred Colin Farrell alongside Angelina Jolie, Val Kilmer, Sir Anthony Hopkins, Jared Leto and Rosario Dawson.