One of the main applications of multi-object tracking in the context of autonomous driving is improving road safety. An accurate environment understanding where pedestrians and vehicles are correctly identified reduce the risk of an accident while driving. However, occlusions produce identification switches and detection errors, which may involve losing track of an object in the images captured by the vehicle. In this context, tracking by detection is the leading solution. Trackers following this architecture employ a Kalman filter for predicting an object location, encoded as a bounding box within the image boundaries. Having access to a posterior state prediction provides useful information for dealing with occlusions. Unfortunately, the Kalman filter is not designed for producing multi-step ahead predictions. In this work we propose the use of Echo State Networks, (ESN) as a modeling alternative to the Kalman filter. Their recursive nature makes ESNs suited for modeling movement patterns of the bounding boxes detected in the image. Performance results are computed by isolating the motion modules from the tracker itself: a perfect object detector is assumed to enable a detailed analysis of the prediction capabilities of each model over specific object tracks and time slots. Experimental results verify the potential of ESNs for accurate multi-step ahead visual motion prediction. The virtual trajectories delineated by the predicted bounding boxes provide valuable information for anticipating occlusions.