The increase in demand for spectrum-based services forms a bottleneck in wireless networks. Device-to-Device (D2D) caching networks tackle this problem by exploiting users behavior predictability and the possibility of sharing data between them to alleviate network congestion. Usually, network congestion occurs at certain times of the day and in some popular locations. Consequently, the information about user's demand alone is not enough. Capturing mobility statistics allows Service Providers (SPs) to enhance their caching strategies. In this work, we introduce a mobility-aware centralized D2D caching network where a SP harnesses users demand and mobility statistics to minimize the incurred service cost through an optimal caching policy. However, the complexity of the optimal caching policy grows exponentially with the number of users. Therefore, we discuss a greedy caching algorithm which has a polynomial order complexity. We also use this greedy algorithm to establish upper and lower bounds on the proactive service gain achieved by the optimal caching policy.