A fiber-reinforced polymer composite is a composite material in which fibers are dispersed in a continuous polymer matrix. Fiber-reinforced composite materials can be prepared by manufacturing processes such as Liquid Composite Molding (LCM), in which a dry fiber structure is infiltrated by a liquid polymer system. The design of such manufacturing processes is supported by process simulation. The flow simulation of a liquid polymer through the fiber structure is governed by flow phenomena at different spatial scales spanning from micrometers (microscale) to meters (macroscale). The first and vital step in this process simulation is the estimation of permeabilities of the fibrous microstructure. The porous media at higher spatial scales (mesoscale, macroscale) are then homogenized using these microscale permeabilities. Presently, conventional methods compute permeability by solving the Stokes equation which governs the fluid flow through the microstructure. However, performing repetitive flow simulations on 3D microstructures require a lot of computational effort and time. Since the flow simulations on higher spatial scales are also expensive, a fast emulator for permeability prediction on the microscale is desirable. Here, modern machine learning and deep learning methods which offer fast inference times have become of great interest. A comprehensive dataset of fibrous microstructures and their numerically computed permeabilities was generated using the commercial solver GeoDict for the task of supervised learning. Each data sample consists of unit cell geometries of synthetic fibrous microstructures, effective parameters characterizing the microstructure geometry and numerically computed permeabilities in various directions. In this work, data-driven emulators were developed using machine learning to predict the permeability of 3D fibrous microstructures based on their geometry. These emulators are designed using 3D convolutional encoders and fully connected layers. The performance of these emulators is compared with existing methods for geometry-based permeability prediction on the benchmark dataset. It is also investigated how well the models generalize in predicting permeabilities of previously unseen fibrous microstructures, outside of the training data distribution. These trained emulators can predict permeabilities at much faster inference times compared to conventional methods.