Is original research required for an undergraduate thesis?
The professor is suggesting you do the final project and keep it easy for both parties. I got data, my name on the paper, and research presentation at academic conference in undergrad by playing ball and working on the professor's pet project.  And just because the school calls it an FYP doesn't mean you have to call it that. I'm not saying you can call it a thesis but if you applied elsewhere, FYP would sound really obscure and student-ish.  If you own a quality piece of written work, you can rework the intro and publish it wherever it fits in your field. If nobody wants to publish it, hold onto it and maybe it can get worked into something else later. Maybe that FYP is "currently submitted" for publication on your CV at just the right time later. Thesis may be property of the school. Final thought: professor may commit time to messing around with data and getting complicated with you if he can co-publish something. It's a lot of extra office hours with you to do a thesis when they could be with their family at home. Can you make it worth their time? Let them hint to you how it can be worth going the extra mile.