Asset monitoring and tracking is an important application of wireless sensor networks (WSNs). Tiny sensors collect information about the assets and convey this message to the base station using multi-hop routing techniques. For instance, in habitat monitoring application, the nodes collect details of the endangered species and report to the central controller, i.e., the base station. Preserving the privacy of these assets from the attackers is imperative. An attacker may backtrack the message flow and eventually capture the asset. In this work, we aim to improve the source location privacy, which is measured by the safety period, by designing a new routing technique where randomized routes in the whole network are generated distributively between the node of origin and the base station. The diversity of the routing paths will lengthen the backtracking period of the attacker and thus increase the safety period. The key feature of the solution is that it achieves improved source location privacy without hampering the network lifetime. Unlike the existing solutions, the proposed technique does not employ any fake sources that decreases the network lifetime due to generation of large number of dummy packets. The solution performs quite well even when the asset is near the base station. The proposed method is analysed and compared with forward random walk and phantom single path routing schemes. Simulation results demonstrate that the proposed method achieves improved privacy level with more uncertainty in the routing paths than the current techniques.