Biological tissues can be conceptualized as porous media, where proliferating tumor cells interact with the extracellular matrix and interstitial fluid. Accurately predicting tumor growth in this environment requires a multiphysics approach that captures coupled biochemical transport, tissue deformation, and fluid flow. In this work, we propose a computational model that integrates these phenomena by combining equations for cellular proliferation and migration, mechanical equilibrium of the tissue, and fluid conservation within the porous matrix. The resulting system is highly coupled and nonlinear, posing challenges for traditional numerical solvers, and similar difficulties arise in scenarios where experimental or clinical data are limited. To address these challenges, we employ Physics-Informed Neural Networks (PINNs), which embed the governing physics directly into the training of neural networks. This approach allows us to predict tumor propagation and the associated tissue mechanics while enforcing consistency with the underlying physical laws. Preliminary results show that the framework can effectively capture tumor growth patterns and tissue deformation, providing a computationally efficient and predictive tool for understanding tumor progression in complex biological environments. This methodology has potential applications in biomedical research and treatment planning, bridging continuum modeling with AI-driven simulations.