Have you considered talking to your best friend and trying to figure out where the rumors are coming from? It may seem like a hard conversation to have but if you want to preserve your friendship being direct may be the best course in a respectful way. I encourage clients to use "I statements" which let the person know which behavior you don't like without attacking them. You could say "I feel sad/disappointed/hurt when you spread rumors about me." Then ask what is going on that caused this behavior. If you are concerned about having the conversation in private maybe choose a semi-public space so that things won't get to out of hand. Good luck!
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Related Questions: My best friend is spreading rumors about me. Its making so sad and mad that I cant leave the house. What do I do?