In this work, we present an optimal sensor placement framework for variable impedance actuated (VIA) robots. Traditionally, sensors are placed on robotic systems to ensure direct measurement of all states. VIA robots have high number of actuators to regulate stiffness, damping and position independently. Therefore, direct measurement of all states requires a high number of sensors increasing the cost, weight and probability of hardware faults. Measuring a subset of states and estimating the rest might be a solution for this problem. However, selecting the subset of states to measure is not straightforward. To tackle this problem, we formulated an optimization problem using the Gramian based observability matrix. The observability of the system with different subsets of sensors is measured for given trajectories and the subset of sensors with the best observability measure is selected. We demonstrated the efficacy of our sensor selection approach in simulation experiments conducted with two variable stiffness actuated robots.