Poly-e-caprolactone (PCL) has been widely used in nanoparticle based drug delivery devices, owing to its hydrophobicity and biodegradability. In this study, we investigated the interaction of single block copolymer chains of PCL and Methoxy-polyethylene glycol (MePEG), as well as the self-assembled nano-polymeric micelles of these copolymers, with a model dioleoylphosphatidylcholine (DOPC) lipid bilayer using coarse-grained molecular dynamics simulations in conjunction with umbrella sampling. Our studies showed that the hydrophilicto- hydrophobic ratio of the micelle plays a crucial role in the interaction with the bilayer. Significant changes in the micelle morphology akin to the 'snorkeling effect' was also observed.