The paper continues the authors’ previous research on the development of high-tech industry in the Eurasian Economic Union (Issues Relating to the Hi-Tech Industry in the Eurasian Economic Union), in which the main features, problems, and ways of development of high-tech bionanoindustry have been determined and the further research areas formulated. In this study, the methodical form of solving previously identified bionanoindustry issues is creating innovative international bionanotechnology (industrial) clusters, including the arrangement of foresight centers within them to ensure convergence of technologies and foresight research and projects in the field of bio- and nanotechnology. To achieve the goal set in the study, a conceptual organizational model of an innovative international bionanotechnology cluster of the Eurasian Economic Union has been developed, the need for creating a foresight center as part of innovative international bionanotechnology clusters justified, and guidelines for its formation and estimation of efficiency elaborated. The further research area is improving the state cluster policy to develop high-tech complexes and scientific justification of creating engineering infrastructure within the innovative international bionanotechnology clusters, including the arrangement of engineering centers within them to provide various engineering services to small and medium-sized innovation enterprises forming the cluster, the performance of joint research and development, the acceleration of transferring technologies to large-scale production, and training staff qualified in bio-nano-oriented engineering.