Usually your first meeting with the supervisor is like that, and they'll probably expect it to an extent. Look at some of the SPECIFIC research papers/projects your supervisor is working on/has worked on in the past. Is there scope for extended work on that, at your undergrad level? Make notes of where this may be possible, and note which areas seem like they'll be beyond the scope of an undergraduate dissertation as well.
Your supervisor will likely have some projects in mind anyway, but they will be very receptive to ideas and appreciate you spending time and thought on it. The latter case mentioned above of topics beyond the scope of UG work is relevant so you can, if necessary, move away from any suggestions they make that might be problematic because of this.
This is not uncommon; we all want to project our best self but it's important to not give false impressions and end up in a project which is way beyond your abilities, and potentially any UGs abilities. This is particularly relevant if your supervisor previously was at a very high tier university e.g. MIT, Oxbridge, Grandes Ecoles; certainly at MIT, CalTech the GEs etc abroad, as a lot of what would be undergrad/UG masters level work there is actually closer to PhD level work at most other places, even respectable RG unis.