Achieving color constancy is an important part of image preprocessing pipeline of contemporary digital cameras. Its goal is to eliminate the influence of the illumination color on the colors of the objects in the image scene. State-of-the-art results have been achieved with learning-based methods, especially when the deep learning approaches have been applied. Several methods that are combining local patches for global illumination estimations exist. However, in this paper, a new convolutional neural network architecture is proposed. It is trained to look for the regions, i.e., patches in the image where the most useful information about the scene illumination is contained. This is achieved with the attention mechanism stacked on top of the pretrained convolutional neural network. Additionally, the common problem of the lack of data in color constancy benchmark datasets is alleviated utilizing the stage-wise training. Experimental results show that the proposed approach achieves competitive results.