Trajectory prediction is an integral component of modern autonomous systems as it allows for envisioning future intentions of nearby moving agents. Due to the lack of other agents' dynamics and control policies, deep neural network (DNN) models are often employed for trajectory forecasting tasks. Although there exists an extensive literature on improving the accuracy of these models, there is a very limited number of works studying their robustness against adversarially crafted input trajectories. To bridge this gap, in this paper, we propose a targeted adversarial attack against DNN models for trajectory forecasting tasks. We call the proposed attack TA4TP for Targeted adversarial Attack for Trajectory Prediction. Our approach generates adversarial input trajectories that are capable of fooling DNN models into predicting user-specified target/desired trajectories. Our attack relies on solving a nonlinear constrained optimization problem where the objective function captures the deviation of the predicted trajectory from a target one while the constraints model physical requirements that the adversarial input should satisfy. The latter ensures that the inputs look natural and they are safe to execute (e.g., they are close to nominal inputs and away from obstacles). We demonstrate the effectiveness of TA4TP on two state-of-the-art DNN models and two datasets. To the best of our knowledge, we propose the first targeted adversarial attack against DNN models used for trajectory forecasting.