Eye movements have long been studied as a window into the attentional mechanisms of the human brain and made accessible as novelty style human-machine interfaces. However, not everything that we gaze upon, is something we want to interact with; this is known as the Midas Touch problem for gaze interfaces. To overcome the Midas Touch problem, present interfaces tend not to rely on natural gaze cues, but rather use dwell time or gaze gestures. Here we present an entirely data-driven approach to decode human intention for object manipulation tasks based solely on natural gaze cues. We run data collection experiments where 16 participants are given manipulation and inspection tasks to be performed on various objects on a table in front of them. The subjects' eye movements are recorded using wearable eye-trackers allowing the participants to freely move their head and gaze upon the scene. We use our Semantic Fovea, a convolutional neural network model to obtain the objects in the scene and their relation to gaze traces at every frame. We then evaluate the data and examine several ways to model the classification task for intention prediction. Our evaluation shows that intention prediction is not a naive result of the data, but rather relies on non-linear temporal processing of gaze cues. We model the task as a time series classification problem and design a bidirectional Long-Short-Term-Memory (LSTM) network architecture to decode intentions. Our results show that we can decode human intention of motion purely from natural gaze cues and object relative position, with $91.9\%$ accuracy. Our work demonstrates the feasibility of natural gaze as a Zero-UI interface for human-machine interaction, i.e., users will only need to act naturally, and do not need to interact with the interface itself or deviate from their natural eye movement patterns.