Rothfuss doesn't know, and Rothfuss doesn't want to guess. He's received a lot of damaging comments about this, and -- believe it or not -- a Reddit AMA on /r/books is actually the authoritative source here.
Rothfuss, about a year ago, asked himself a question on one of his AMAs, which I'll transcribe here for convenience. The empahsis is mine - you can just read the bold lines to get the gist of it:
Hey there Pat, I really love the first two books in your series.
I know it takes time to produce quality books (especially books of the size you tend to write, which are easily 2-3 times larger than many other novels). But still, I'm quite eager for the third book. Do you happen to have a publication date?
Thanks for asking Pat,
Unfortunately, there is no publication date right now. What's more, I really don't want to guess at one.
You see, when the first book came out, I was very new to publishing, and I foolishly told people they could expect the next book in a year.
Later, when I realized I needed more time to make the second book as perfect as I could, I was forced to break that promise, and people were unhappy. And this is understandable: They felt as if they'd been lied to.
I'm trying to avoid making that mistake again. I screw up constantly, but I try to avoid fucking up in the same way twice in a row.
Rest assured that when there is a publication date. I'll make a big announcement.
So, no. He hasn't, and won't, talk about it. He gives another self-reply, which explains why it's taken so long, and why he wishes people would stop asking about it:
Thanks for the quick answer, Pat.
I'll admit I'm a little disappointed at the lack of a firm date, but I appreciate your artistic integrity and your desire to give us the best book possible.
Also, while it's true that my interaction with you almost entirely revolves around the books you produce, I also recognize that you are a fellow human being. I imagine that you are similar to me in that you have a busy and complex life.
While I enjoy your books a great deal, I'm guessing that being the father of two young boys takes up a great deal of your time, to say nothing of the charity which you help manage.
And while I'd like nothing better than to read a hundred billion books from you, I'm guessing you probably have hobbies, too. I respect that. You probably like playing video games, watching movies with friends, and occasionally walking somewhere with no purpose at all, other than enjoying the feel of cool spring grass beneath your feet.
He did this mostly to get this question out of the way, because it was one people were guaranteed to immediately ask. And then refused to say anything else about the topic.