Harris starred in the first two Harry Potter films and was replaced by Michael Gambon for the rest of the series.
Asked if he could have played Dumbledore, Sir Ian told HARDtalk: "Well, sometimes when I see posters of Michael Gambon, the actor who gloriously plays Dumbledore, I think it's me. You know, we get asked for each other's autographs!"
Meanwhile, Sir Ian has called on other gay actors to follow his example and make their sexuality known publicly. The award-winning star - who first revealed he was gay in 1988 - claimed actors could set an example to those young people who are confused about their sexuality, and ultimately, help them to live a happier life.
He said: "Practically every person I know who has declared their sexuality, life becomes better in every possible way once you are honest."
-Bang! Showbiz