Advances in communication technologies and connected vehicles provide excellent opportunities for data exchange between vehicles and infrastructure. The data transmitted by connected vehicles offers valuable information to traffic control centers to improve the safety and operation of the transportation network. However, there are some security concerns associated with the data communicated between vehicles and infrastructure that may affect the privacy of connected vehicle users. The objective of this study is to assess the privacy of connected vehicles concerning the feasibility of reconstructing the travel path of the vehicles from the basic safety messages exchanged between vehicle and infrastructure. This study adopts a mathematical programming approach to identify the paths of vehicles based on their location, speed, and heading. An iterative algorithm is proposed to reconstruct the path of a vehicle, based on the assumption that the new state of the vehicle can be predicted from its previous state. The performance of the proposed algorithm is also evaluated with the increase in the number of vehicles and overlapping paths.