The ligand-receptor-mediated contacts of small sub-100-nm-sized lipid vesicles (or nanoparticles) with the cellular membrane are of interest in the contexts of cell-to-cell communication, endocytosis of membrane-coated virions, and drug (RNA) delivery. In all these cases, the interior of vesicles is filled by biologically relevant content. Despite the diversity of such systems, the corresponding ligand-receptor interaction possesses universal features. One of them is that the vesicle-membrane contacts can be accompanied by the redistribution of ligands and receptors between the contact and contact-free regions. In particular, the concentrations of ligands and receptors may become appreciably higher in the contact regions and their composition may there be different compared to that in the suspended state in the solution. A statistical model presented herein describes the corresponding distribution of various ligands and receptors and allows one to calculate the related change of the free energy with variation of the vesicle-engulfment extent. The results obtained are used to clarify the necessary conditions for the vesicle-assisted pathway of drug delivery.