The two-dimensional irregular packing problem is an NP-hard challenge, notorious for requiring sophisticated strategies to optimize object placement for maximizing area utilization while minimizing waste. Traditional heuristic algorithms rely on complex calculations of placeable and non-placeable areas, which can hamper efficiency. This paper introduces an exploratory study using UNet-based architectures, traditionally successful in medical image segmentation, to approximate these calculations in packing scenarios. We present two adaptations, NFP-UNet-R18 and NFP-UNet-R34, which incorporate residual blocks to potentially refine the learning of placeable area patterns. Initial results demonstrate that these models can learn to identify placeable areas and achieve reasonable utilization, albeit limited by the amount of training data available. These findings suggest that with further development and more extensive training, UNet-based methods could significantly enhance computational efficiency in industrial applications.