How to disclose salary requirements without risking a job offer?

As some of you all know, I’ve been a temp for over a year and I’m tired of being strung along. I finally have an interview with a university and it has great benefits. The job sounds good and pay is decent in my opinion. I make $16.50/HR right now, probably if I stick around another month or two it’ll jump to $17–17.50.

The position I’m interviewing for is starting at $37,000 which is a tad more than what I’m making but I would like to request maybe $19–20/HR range but in truth, I would take the $37,000 anyway. They disclosed the salary to me, if they ask me what kind of pay I am looking for do I keep it vague and say “It’s negotiable”? I know that this response has annoyed many. Jobs nowadays ask for your previous pay, so they know what I’m making right now. I’d like to make $40,000 to be honest. I’d be happy with a $18/HR although it’ll only be $60 more in a pay check.