I suspect Hollywood is responsible, so I suppose this might be a question directed towards film or entertainment historians, rather than fellow medievalists.
It comes from India/Sri Lanka where fortresses sometimes had estuarine crocodiles (such as at Sigiriya in Sri Lanka).
At Sigiriya (A UNESCO site) they have information boards about the location and one of them discusses the crocodiles in the moat and how the story made its way to Europe.
No quotable source unfortunately.
While I'm not a film historian, the Tower of London had menagerie that held all sorts of exotic creatures. I want to say that Richard the lionhearted supposedly brought back crocodiles from the crusades, I however can't remember for the life of me where I read that so I can't cite it (Source below). It may have derived from that. The menagerie held lions, bears, and other exotic animals. It could have begun with that.
This is a new one on me... do you have an example?