Graphical user interface (GUI) grounding is a key capability for computer-use agents, mapping natural-language instructions to actionable regions on the screen. Existing Multimodal Large Language Model (MLLM) approaches typically formulate GUI grounding as a text-based coordinate generation task. However, directly generating precise coordinates from visual inputs is challenging and often data-intensive. A more intuitive strategy is to first identify instruction-relevant visual patches and then determine the exact click location within them. Motivated by recent observations that general MLLMs exhibit native grounding ability embedded in their attention maps, we propose GUI-AIMA, an attention-based and coordinate-free supervised fine-tuning framework for efficient GUI grounding. GUI-AIMA aligns the intrinsic multimodal attention of MLLMs with patch-wise grounding signals. These signals are calculated adaptively for diverse user instructions by multi-head aggregation on simplified query-visual attention matrices. Besides, its coordinate-free manner can easily integrate a plug-and-play zoom-in stage. GUI-AIMA-3B was trained with only 509k samples (around 101k screenshots), demonstrating exceptional data efficiency and verifying that light training can trigger the native grounding capability of MLLMs. It achieves state-of-the-art performance among 3B models, attaining an average accuracy of 61.5% on ScreenSpot-Pro, 92.1% on ScreenSpot-v2, 68.1% on OSWorld-G, 79.1% on MMBench-GUI-L2, and 60.0% on UI-Vision. Project page: https://github.com/sjz5202/GUI-AIMA