Prediction plays an important role in the visual perception of moving objects. Prior studies using multivariate pattern analyses have shown that the neural representation of an object’s position is updated based on predictions about its current and future positions along its motion trajectory. Thus far, this evidence for extrapolation has only been reported for explicitly tracked objects, i.e., that are the target of attention. However, it is unknown whether extrapolation also occurs for visible but unattended moving objects, i.e., not explicitly tracked. To investigate this possibility, we used a novel paradigm that could enable spatial positions of tracked and non-tracked moving objects to be independently decoded from time-resolved EEG activity. Participants simultaneously viewed two objects, distinguished by color, and were instructed to track one while ignoring the other. The objects moved in apparent motion around a circle, appearing every 100ms along unrelated trajectories. At each timepoint, there was a superposition of neural activity from both objects with information about their current and prior spatial positions and, putatively, their future, extrapolated positions. Using time-resolved position classifiers, it was possible to decode the current and prior positions of the non-tracked (and tracked) object from 2ms snapshots of neural activity. Crucially, the future position of the non-tracked object was not decodable. This was, however, not the case for the tracked object. Our findings suggest that top-down attention might be necessary for motion prediction. Accounting for how attention and prediction influence each other is an important priority for future studies of visual motion tracking.