Pedipulation leverages the feet of legged robots for mobile manipulation, eliminating the need for dedicated robotic arms. While previous works have showcased blind and task-specific pedipulation skills, they fail to account for static and dynamic obstacles in the environment. To address this limitation, we introduce a reinforcement learning-based approach to train a whole-body obstacle-aware policy that tracks foot position commands while simultaneously avoiding obstacles. Despite training the policy in only five different static scenarios in simulation, we show that it generalizes to unknown environments with different numbers and types of obstacles. We analyze the performance of our method through a set of simulation experiments and successfully deploy the learned policy on the ANYmal quadruped, demonstrating its capability to follow foot commands while navigating around static and dynamic obstacles. Videos of the experiments are available at sites.google.com/leggedrobotics.com/perceptive-pedipulation.