Polymers are the most common packaging materials used for food, beverages, cosmetics, and other consumer products. The ever-growing concern over pollution generated from single-use packaging materials, and the ensuing potential environment contamination resulting from their use has raised safety questions. Polymers used in these materials are often not spared from the presence of impurities, including unreacted monomers and small oligomers. The characterization of transport properties, including diffusion and leaching of these penetrant molecules is largely hampered by the long timescales involved in shelf-life experiments. In this work, we employ molecular simulation techniques to explore the main mechanisms involved in the bulk and interfacial transport of monomer molecules from three polymers commonly employed as packaging materials: polyamide-6, polycarbonate, and poly(methyl-methacrylate). Our simulations shed light on the main diffusion mechanisms for in- and outbound penetrant diffusion and provide rationalization for monomer leaching in model food formulations as well as bulky industry-relevant molecules. With these molecular-scale characterization we provide base insights to aid the design of polymer/consumer product interfaces with reduced risk of contamination and longer shelf-life.