The recent success of immersive applications is pushing the research community to define new approaches to process 360° images and videos and optimize their transmission. Among these, saliency estimation provides a powerful tool that can be used to identify visually relevant areas and, consequently, adapt processing algorithms. Although saliency estimation has been widely investigated for 2D content, very few algorithms have been proposed for 360° saliency estimation. Towards this goal, we introduce Sphere-GAN, a saliency detection model for 360° videos that leverages a Generative Adversarial Network with spherical convolutions. Extensive experiments were conducted using a public 360° video saliency dataset, and the results demonstrate that Sphere-GAN outperforms state-of-the-art models in accurately predicting saliency maps.