Should I show employers my abundance mentality (I have other employers as options) or should I show one employer that I'm loyal?

I will be starting an internship at a bulge bracket bank soon, and I am hoping they will offer me a full time position after the internship ends. I don't want to work anywhere else, it's the perfect place to start my career. How do I show them that I only want to work in their firm without appearing needy?