A sentence on this website reads:
It might well be, implies the narrator, that he made up the whole story, but he's content to leave it up to the reader to decide which "passages" of his story are true and which are entirely fictional.
More examples can be picked from Google Books.
My intuition is that "implies the narrator" is structurally equivalent to "says the narrator", which is an instance of quotative inversion. Nonetheless, it appears that, unlike say, imply cannot be used to introduce direct quotes.
What is the grammar behind "implies the narrator"?