This paper presents a novel biologically-inspired visual servoing framework that enables a robot arm to reach previously unseen objects without requiring robot or camera calibration. Our framework consists of an “eye” that estimates the approximate position of the target object, and a “brain” that guides the robot arm to reach the object through iterations of eye estimation and action. To this end, we train an estimator to estimate the position difference between the target view and the current view in an “eye-in-hand” setting. Furthermore, we introduce a reinforcement learning-based policy network to guide the robot arm with the estimation information. Our experimental results demonstrate that the proposed framework is plausible, and has the potential for real-world deployment due to its ability to reduce the observation space and accelerate the training process.