OMG do NOT mention it!!! They not only don't care, but it will make you look immature. You're supposed to want to go there because you like the school. And honestly, that's a dumb reason for transferring. If you and your girlfriend love each other that much and trust each other, college won't break you up. I know someone who didn't do an exchange program to France because she was dating someone she thought she was going to marry, and she ended up breaking up with him and completely missed out on going to France. She is SO kicking herself for it.
You might end up staying with your girl throughout college or not, but that is definitely not a reason to transfer. School is so much bigger than that, and it affects your career. Don't do it.