Mobile Edge Computing (MEC) technology has been introduced to enable could computing at the edge of the network in order to help resource limited mobile devices with time sensitive data processing tasks. In this paradigm, mobile devices can offload their computationally heavy tasks to more efficient nearby MEC servers via wireless communication. Consequently, the main focus of researches on the subject has been on development of efficient offloading schemes, leaving the privacy of mobile user out. While the Blockchain technology is used as the trust mechanism for secured sharing of the data, the privacy issues induced from wireless communication, namely, usage pattern and location privacy are the centerpiece of this work. The effects of these privacy concerns on the task offloading Markov Decision Process (MDP) is addressed and the MDP is solved using a Deep Recurrent Q-Netwrok (DRQN). The Numerical simulations are presented to show the effectiveness of the proposed method.