Deal with, don't avoid, rumors. People will create information to fill gaps in their understanding. If you do not communicate early and frequently people will make up or listen to things that may be incorrect. Rumors are a normal response to change and not an aberrance. Top Address the organization's history.
People interpret the information they receive based, in part, on past experience.
What is the history of the vehicle you are using to communicate and what is the impact of this history on credibility. For example, if past communications denied that anything was changing, but they did, people will lose trust. If people were informed that the coming changes were small, but they were, in fact, significant, they have reason to doubt what they hear. Consider the organization's history when communicating to people and address this concern directly. Get help now.