Crowd navigation has received increasing attention from researchers over the last few decades, resulting in the emergence of numerous approaches aimed at addressing this problem to date. Our proposed approach couples agent motion prediction and planning to avoid the freezing robot problem while simultaneously capturing multi-agent social interactions by utilizing a state-of-the-art trajectory prediction model i.e., social long short-term memory model (Social-LSTM). Leveraging the output of Social-LSTM for the prediction of future trajectories of pedestrians at each time-step given the robot's possible actions, our framework computes the optimal control action using Model Predictive Control (MPC) for the robot to navigate among pedestrians. We demonstrate the effectiveness of our proposed approach in multiple scenarios of simulated crowd navigation and compare it against several state-of-the-art reinforcement learning-based methods.