In this paper, we consider a multi-server content-centric networking (CCN) architecture, where the servers have distinct trust credentials toward the user while the requested files convey the user's personal information. The servers can infer personal information when serving the user such that privacy concerns are triggered. Unlike the pre-processing and protocol-based solutions in literature, e.g., encryption, requiring additional processing or lacking quantitative information leakage measure, in this paper, an optimization-based collaborative content delivery strategy is developed to minimize the information leakage to the servers in the content delivery phase. Gaussian mixture model (GMM) is used to construct the user profile and the file contents. We leverage Kullback Leibler (KL) divergence between the exact and estimated user profiles to measure the privacy leakage. The formulated non-convex mixed-integer program is solved with a polyhedral outer approximation (POA) algorithm. We show that our scheme ultimately reduces information leakage over random content delivery while approaching the probabilistic method.