Managing cache content at the edge is one of the many use cases of 5G-And-beyond networks. However, increasing the density of Edge Data Centers (EDCs) to service requests is a crucial problem. To overcome this problem, recent research has advanced mobile device architecture paradigms and the content caching in a Mobile Device Cloud (MDC). These two service locations (EDCs and MDC) are registered with the Mobile Network Operator (MNO), enabling the MNO to control the content placement for profit maximization. As the user demands for content items are directly related to the QoS perceived by the user, it is important to understand the future popularity of the content items and to place them appropriately. Additionally, privacy issues have increased over time because of sensitive user information being divulged at the MDC. To preserve privacy, a branch of machine learning called Federated Learning (FL) can train machine learning models leaving the data in the end user devices. The paper contributions are as follows: (1) We introduce an FL algorithm called FedCo, that trains a deep-neural network (DNN) to predict the user demand of a specific content, so as to manage the content files placement at EDC and MDC sites. (2) We then conduct a theoretical evaluation of user demand behavior via prospect theory to justify revenue maximization for an MNO. (3) We show numerically via a multimedia content delivery use-case how the proposed model compares favorably with two state-of-The-Art designs.