Stone said he would make a movie in India "if there was a great story".
He said Indian cinema was "very prolific and vital" and that he had used that vitality in his 1994 film Natural Born Killers.
The movie is about two young lovers who commit numerous robberies and murders during a wild three-week spree.
Stone is in the western Indian city of Mumbai (Bombay) to receive a lifetime achievement award at a prominent film festival.
"Indian cinema is very prolific. I can't keep up. I used that vitality in Natural Born Killers. I love that the films switch from comedy to romance and then to tragedy. I love that," Stone told reporters.
He said he had studied Indian filmmaker Satyajit Ray's works in school.
Asked if he would make a movie in India, Stone said: "If there was a great story. If I had Danny Boyle's luck, I'd make Slumdog Millionaire. There was a good detective story [based in India] written two years ago but..."
Stone shot parts of his film Alexander in the Ladakh region which he described as "beautiful".
Stone said his 10-part documentary mini-series, The Untold History of America, will air sometime next year.
Oscar-winning director Oliver Stone says he loves Indian cinema for "being able to switch between comedy, romance and tragedy at the same time".