Absolutely you can negotiate - and honestly, I'd say it's worth trying even if the listing agent says the seller won't budge. That's kind of their job to say that, you know? I've seen sellers claim they won't negotiate and then suddenly they're willing to come down when a solid offer comes in. The market matters a lot though - if it's a hot market with tons of offers, yeah, sellers have leverage. But if things have been sitting for a bit or it's a slower time of year, you've got more room to work with.
Here's the thing: make a reasonable offer based on comps in the area, get your surveyor involved so you've got ammunition if there are issues, and include a personal letter or whatever helps you stand out. Don't lowball it so hard they just reject you outright, but there's definitely space between asking price and what they might actually accept. I'd start somewhere like 5-8% below asking depending on your local market - your own agent should be giving you advice on what's realistic in your area. Even if they won't budge much, you might get them down a few grand, or they could throw in repairs or cover some closing costs instead.
The worst that happens is they say no, right? But I've negotiated on probably 70% of the deals I've seen go through. Just don't get emotionally attached to this one place - there's always another house out there if they truly won't work with you.