Camera model identification is paramount to verify image origin and authenticity in a blind fashion. State-of-the-art techniques leverage the analysis of features describing characteristic footprints left on images by different camera models from the image acquisition pipeline (e. g., traces left by proprietary demosaicing strategies, etc.). Motivated by the very accurate performance achieved by feature-based methods, as well as by the progress brought by deep architectures in machine learning, we explore in this paper the possibility of taking advantage of convolutional neural networks (CNNs) for camera model identification. More specifically, we investigate: (i) the capability of different network architectures to learn discriminant features directly from the observed images; (ii) the dependency between the amount of training data and the achieved accuracy; (iii) the importance of selecting a correct protocol for training, validation and testing. This study shows that promising results can be obtained on small image patches training a CNN with an affordable setup (i. e., a personal computer with one dedicated GPU) in a reasonable amount of time (i. e., approximately one hour), given that a sufficient amount of training images is available.