Cooperative cellular networks is productive approach to improve network system capacity, network reliability, data rate, and also increases the hold of spectrum resources in the fifth generation (5G) networks. For this purpose, selection of a relay in cooperative communication has been widely investigated in the past few years and with research in vehicular network, the selection of mobile relay has been studied. In cooperative communication, operator (base station) assigns mobile relay to each mobile user in order to minimize total transmission power and cost with improved data rates. The relay selection is based upon the utilities or benefits provided to three players, i.e. operator, mobile user (MU) and mobile relay (MR). Incentives must be given to mobile relays to make them cooperate for their utilized resources. Despite much effort that has been made in cooperative communication, mobility of a mobile relay along with selection and defining utility gains for three players involved is still left as an open research problem. In this paper, we propose an auction based scheme for relay selection in cooperative communication. For this purpose, we formulate utilities of three players while considering mobility of a mobile relay. Based on the random waypoint mobility model, a centralized Predicted Mobility Based Profitable Relay Selection Algorithm (PMPRSA) is proposed by using auction theory to select a mobile relay. Performance analysis shows that the proposed PMPRSA selects a mobile relay while providing higher data rate and incentives to all three players for their shared resources.