Untitled Book
Although it is not 100% certain that a third Alienist book is being released, there have been mentions of such a book in different articles over the years. The most compelling evidence is found in an article by The Age which can be read at this location. On the last page of the interview (right at the bottom) you will see a small mention that Caleb Carr is "currently working on third Alienist novel".
Up until April of 2006, it looked as though this book may have been getting released later in 2006 based on an Amazon.com listing for an "Untitled Alienist Audiobook". However, recently, this same listing has been removed making it difficult to predict when, or if, the third book is going to be published.