Traditional network infrastructure is facing significant challenges to support the growing bandwidth, coverage, and latency requirements of users, and to support new 4G and 5G use-cases. As a solution, telecom operators are looking to implement Network Function Virtualization (NFV) in future networks. The placement of Virtual Network Functions (VNFs) plays a critical role in reducing latency to serve users, while also helping in reducing the overall operational cost of the network. This work focuses on the VNF placement problem in the context of mobility and handovers, in scenarios such as mobile users travelling at high speeds, users served by small cells, and mobile IoT devices. We have modelled the VNF placement problem as an optimization problem that aims to reduce the latency in handovers resulting from mobility. We have compared our approach with other approaches, and we have demonstrated upto 60% reduction in the average time taken to serve handover requests in the network with no considerable increase in overall operational cost. We also provide a sub-graph based approach to solve for larger topologies and demonstrated its scalability.