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Spatio-temporal video grounding (STVG) aims at localizing the spatio-temporal tube of a video, as specified by the input text query. In this paper, we utilize multimodal large language models (MLLMs) to explore a zero-shot solution in STVG. We reveal two key insights about MLLMs: (1) MLLMs tend to dynamically assign special tokens, referred to as \textit{grounding tokens}, for grounding the text query; and (2) MLLMs often suffer from suboptimal grounding due to the inability to fully integrate the cues in the text query (\textit{e.g.}, attributes, actions) for inference. Based on these insights, we propose a MLLM-based zero-shot framework for STVG, which includes novel decomposed spatio-temporal highlighting (DSTH) and temporal-augmented assembling (TAS) strategies to unleash the reasoning ability of MLLMs. The DSTH strategy first decouples the original query into attribute and action sub-queries for inquiring the existence of the target both spatially and temporally. It then uses a novel logit-guided re-attention (LRA) module to learn latent variables as spatial and temporal prompts, by regularizing token predictions for each sub-query. These prompts highlight attribute and action cues, respectively, directing the model's attention to reliable spatial and temporal related visual regions. In addition, as the spatial grounding by the attribute sub-query should be temporally consistent, we introduce the TAS strategy to assemble the predictions using the original video frames and the temporal-augmented frames as inputs to help improve temporal consistency. We evaluate our method on various MLLMs, and show that it outperforms SOTA methods on three common STVG benchmarks.