We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of \( p \)-Laplacian type and a linear drift, for which we prove existence and uniqueness using nonlinear semigroup methods and the doubling variables technique. Our main result shows that, as \( p\to\infty \), the weak solutions of the \( p \)-problem converge to a solution of the congested crowd motion problem.