I applied to a position at a well established company (with a specific target range in mind). We discussed expected salary early on. When my expectations were quite a lot over their budget they initially passed on moving me forward. Only after a few weeks the recruiter reached back out to explain my salary expectations were too high. That is when I brought my expected base salary range down by about 10% so I can move forward with the interviewing process.
I passed all interview stages and now have an offer pending. Before the recruiter submitted the offer for 'processing' they asked what are my thoughts about the base salary they would like to offer me. I explained that I'd need to see the offer in writing to make a final decision but if possible I'd like the base salary to be a bit higher. The recruiter said she will submit a request and try to ask for it.
Yesterday the recruiter called by surprise, said the offer is processing 'as-if' we never spoke. She explained the initial base salary in the offer and asked my thoughts -- again, I didn't want to negotiate anything until I have an offer in writing. It sounded like she almost expected me to negotiate but I didn't want to do that before having an offer in writing. Plus the offer is a bit higher than glassdoor's high range, which makes me hesitant if I even should negotiate at this point.
My question is, taking everything in to consideration, the initial conversation, glassdoor salary range and this stage in the process (waiting for written offer), should I and does it make sense to try and negotiate the offer?