You should always try to come from the frame of you being excited about the opportunity and first want to make sure it's a good fit. The onus isn't on you to give a number, and in fact it's pretty ridiculous for them to demand it.
If you've reached the final stages you should be getting an offer letter with a salary amount and then you can negotiate from there. That not happening sounds strange.
With all that said it's pretty straightforward to use a site like glassdoor to see what salaries are at similiar jobs in the area. I see you made a new account just to ask this, iss this a larger company?