KV cache compression is essential for scaling large language models to long-context inference. However, existing methods excel at explicit retrieval tasks but often degrade on tasks that require multi-step reasoning over dispersed evidence. We present **ClueKV**, a training-free KV cache compression framework that better preserves the reasoning-supportive clues under tight cache budgets. The core design of ClueKV is a self-guided, adaptive headwise token reweighting mechanism. Specifically, ClueKV first uses contrastive probability shifts between the query-conditioned context and a context-free reference to construct an unsupervised clue signal, which highlights context tokens supportive of downstream reasoning under the current input. This signal then serves as self-generated guidance for compression. Based on this signal, ClueKV dynamically identifies, for each input instance, the attention heads that are more aligned with reasoning-relevant context regions, and reweights token importance head by head before KV eviction. Across LongReason, LongBench, and RULER, ClueKV consistently outperforms strong KƒV compression baselines, with the largest gains on complex reasoning tasks. On LongReason, it retains 99.21% of full-KV accuracy at a 50% cache budget, and remains more stable than prior methods as context length increases to 64k tokens. ClueKV also introduces only marginal prefill overhead, making it practical for long-context deployment.