Recent advances in deep learning have allowed Artificial Intelligence (AI) to reach near human-level performance in many sensory, perceptual, linguistic or cognitive tasks. There is a growing need, however, for novel, brain-inspired cognitive architectures. The Global Workspace theory refers to a large-scale system integrating and distributing information among networks of specialized modules to create higher-level forms of cognition and awareness. We argue that the time is ripe to consider explicit implementations of this theory using deep learning techniques. We propose a roadmap based on unsupervised neural translation between multiple latent spaces (neural networks trained for distinct tasks, on distinct sensory inputs and/or modalities) to create a unique, amodal global latent workspace (GLW). Potential functional advantages of GLW are reviewed, along with neuroscientific implications.