We aim to realize a robotic system that hands over a necessary object to a user as soon as he/she attempts to reach out his/her hand for it. In order to realize such system, the following is required: 1) detection of the reaching movements, 2) prediction of the target object among multiple objects, and 3) handing-over the object to a user. In this paper, the first two of them are discussed. To detect the reaching movements, we use the speed of a hand movement, the smoothness of the hand trajectory, and the relation between a position of hand and a gaze point. To predict the target object, we use a probabilistic model based on the user's hand movements and his/her gaze direction. The proposed system can detect reaching movements and predict the target object at a very early stage. A description of the experimental results demonstrates the advantage of the method proposed here.