The capture of innovation and the increasing need to innovate lead companies to implement new management practices of inter-organizational relationships. Innovation through Purchasing becomes a major issue, both for the public authorities who want to see the start-ups they have incubated in nurseries of all kinds, and for the large groups who see it as a key to leverage the creative potential and create value for their markets. The capture of innovation, small and medium enterprises (SMEs) including start-ups, by the Purchasing function is a new problem whose description is at the center of researche papers. The integration of start-ups and SMEs in the value chains of large structures raises multiple problems: incompatibility of processes (legal, financial, industrial ...), lag in the maturity of functions, security of industrial property. The article proposes a review of the current literature on the subject and the result consists in proposing and discussing a management model of the relationship between the purchasing function and the SMEs, likely to increase the capture of the innovation. The aim of this paper is to propose a better understanding on the subject, with a view to improving, the management tools allowing to reduce the risks associated with the outsourced development of innovation.