An algorithm to search for a kinematically desired robotic grasp pose with rolling contacts is presented. A manipulability measure is defined to characterize the grasp for multi-fingered robotic handling. The methodology can be used to search for the goal grasp pose with a manipulability ellipsoid close to the desired one. The proposed algorithm is modified to perform rolling-based relocation under kinematic constraints of the robotic fingertips. The search for the optimal grasp pose and the improvement of the grasp pose by relocation are based on the reduction of the geodesic distance between the current and the target manipulability matrices. The algorithm also derives paths of the fingertip on the object surface in order to achieve the goal pose. An algorithmic option for the process of searching for a suitable grasp configuration is hence achieved.