In cultural heritage, various methods have addressed three-dimensional (3D) digitization and reconstruction using two-dimensional (2D) images, including shape from structured light, shape from stereo, and structure from motion. A common challenge is the recognition of the distance of objects in a scene from the viewpoint, usually called depth. Recognizing depth in 2D photographs remains a challenge in computer vision. Deep Learning techniques have improved this area, particularly in what is called monocular depth estimation. This work investigates the applicability of state-of-the-art monocular depth estimation methods as a preliminary step toward complete and automated 3D reconstruction of cultural heritage artifacts. As image-based 3D reconstruction is extremely time-consuming and expertise-demanding, monocular depth estimation methods could provide significant advantages in speeding up the overall process. Our preliminary experiments yield promising results, with a mean accuracy of 88.15%, a mean RMSE error of 37.35, and a mean PSNR of 27.37 dB across these methods.