We propose a segregation model incorporating mobility constraints to make agents select their location based on distance and location relevance. This study fills this gap by designing a segregation model that considers mobility constraints and exploring how they influence segregation dynamics. Drawing on the gravity law of human mobility, our model allows unhappy agents to select the next location to move based on distance and location relevance. Our findings reveal that mobility-constrained models exhibit lower levels of segregation than the Schelling model, albeit with a longer convergence time, and that agents that end in the periphery are more segregated than those in the grid centre. We attribute these phenomena to a small group of persistently unhappy agents from the minority group who gravitate towards the grid centre due to the preference for nearby and relevant locations imposed by mobility constraints.