We present a reward-predictive, model-based learning method featuring trajectory-constrained visual attention for use in mapless, local visual navigation tasks. Our method learns to place visual attention at locations in latent image space which follow trajectories caused by vehicle control actions to later enhance predictive accuracy during planning. Our attention model is jointly optimized by the task-specific loss and additional trajectory-constraint loss, allowing adaptability yet encouraging a regularized structure for improved generalization and reliability. Importantly, visual attention is applied in latent feature map space instead of raw image space to promote efficient planning. We validated our model in visual navigation tasks of planning low turbulence, collision-free trajectories in off-road settings and hill climbing with locking differentials in the presence of slippery terrain. Experiments involved randomized procedural generated simulation and real-world environments. We found our method improved generalization and learning efficiency when compared to no-attention and self-attention alternatives.