Breast density is a crucial biomarker for predicting BC risk and recurrence. Women with dense breast tissues have a higher likelihood of developing BC, and dense tissue can obscure lesions, reducing detection sensitivity. Mammograms are vital for evaluating breast density, typically classified using the BI-RADS system. The main challenge in breast density segmentation is accurately localizing dense tissues. While segmentation models require detailed pixel-wise annotations, obtaining these labels is time-consuming and requires medical expertise. This paper proposes a weakly supervised approach for breast density localization, allowing deep neural network classifiers to generate saliency maps that highlight dense tissue regions based on image-level labels. We validate this model on the RSNA dataset and achieve a Dice score of 0.754, comparable to state-of-the-art supervised methods.