The Rum Diary actor said that although he was excited to "dive into the role", Disney executives simply could not "understand" the direction he was taking the character in.
"I'm very happy to explore all possibilities of a character and really, you know, dive into the role," he told Larry King in a CNN special. "They couldn't understand what I was doing. You know? To the point where Disney wanted to - wanted to fire me. They didn't understand the character. They were actually contemplating subtitling the film."
Depp went on to describe the original Pirates of the Caribbean as "the most important" film of his career, adding that he was interested in exploring Captain Jack for a fifth instalment of the franchise.
"I still feel like in terms of character, Captain Jack is one that I'd like to explore," he said. "Because he's fun. It's his fun. It's a license to be totally and utterly irreverent and get away with it."
It was revealed earlier this month that Depp made $350m (£219m) from the Pirates of the Caribbean series, making him the highest-paid actor in Hollywood.