Office trouble maker

Hi, I need some advice on a work related issue. A couple of weeks ago people in my office started approaching me telling me that a girl was spreading rumors about me and the guy she is dating. Apparently she saw us speaking in the cafeteria and said we were flirting. I thought it would blow over but i still continue to hear about it.I have worked with the guy for 8 years now and we have always had a friendly work relationship and have casual conversation frequently. I have always been extremely private at work and stay away from gossip and drama. It makes me furious that she is telling so many people this when i have made a good name for myself within the company. Should i report her to HR or will that make the situation worse?