I have been working with qualitative (semi-structured) interviews for years and I read a lot of literature that uses such data. I am neither aware of any rule that prohibits or any convention that discourages quoting interview statements before the methodology section/chapter; nor could I see any reason for such a rule to exist. It makes sense to describe the methodology before the analysis and results sections, in which you will draw on your interviews most extensively, but individual interview quotes are not equal to "analysis" or "results". They are just that: Quotes. I would also add that a catchy interview quote can be a good way to introduce a paper/book or to illustrate an empirical result or theoretical conjecture.