As s generalization of semi-invariant Riemannian maps, B. Sahin first introduce the idea of "Generic Riemannian Maps" in the article "Generic Riemannian Maps". He considered the total space as a Kaehler manifold. We extend the notion of generic Riemannian map to the case when the total manifold is nearly Kaehler manifold. We study the integrability conditions for the horizontal distribution while the vertical distribution is always integrable. We also study the geometry of foliation of two distributions and obtain the necessary and sufficient condition for generic Riemannian maps to be totally geodesic. Additionally, we study the generic Riemannian map with umbilical fibers.