Dumbledore clearly suspects Harry might be behind Azkaban. In fact, he says as much. However he doesn't "know".
Dumbledore certainly doesn't "say" that he knows. But as readers we are not shown his internal thoughts (in contrast to Harry, Hermione, Mcgonagall, and many others). Dumbledore's thoughts have been deliberately made opqaue to readers. So we can't definitively say that he knows or doesn't know something. We can only infer which is more likely given other known facts.
I will note on a meta level though, that one possible reason not to show a character's thoughts is that they are thinking and saying different things.
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 94. The previous thread has passed 200 comments.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: