Communication groups in mobile messaging applications (MMAs) multiply the data transmissions, because every message has to be delivered to all members of the communication group. Thereby, they put a high load on mobile networks. As the number of recipients is still comparably small, the data-intensive user-generated content cannot be handled efficiently in large content delivery networks. However, small communication groups, such as groups of friends or teams, might often be in close proximity, which can be leveraged to locally deliver messages by applying edge caching or device-to-device (D2D) communication. In this work, a simulation study is conducted to investigate these potential traffic savings in the mobile network. It is based on a realistic communication model of the MMA WhatsApp and utilizes different models for human mobility. The user mobility and MMA communication are simulated for a single day in a small city to obtain the ratio of messages, which could be potentially transmitted locally when utilizing edge caching and D2D communication.