Kontsevich's deformation quantization of Poisson manifolds suggests a relation to certain topological open strings, as detailed by Cattaneo and Felder. This model has a natuaral generalization to higher dimensional theories, in particular to open membranes. The corresponding model in general deforms a structure of (quasi-)Lie bialgebra, or more precisely a Courant algebroid. The quantization of such objects is still an open problem. Using the open membrane model we propose a road to quantization based on path integral methods and Feynman diagrams. The geometric structure of the open membrane model naturally reflects the super-geometry found in the study of Courant algebroids and reflects the geometric operad corresponding to the deformation theory.