Building effective tokenizers for multilingual Large Language Models (LLMs) requires careful control over language-specific data mixtures. While a tokenizer's compression performance critically affects the efficiency of LLM training and inference, existing approaches rely on heuristics or costly large-scale searches to determine optimal language ratios. We introduce Tokenizer Regression for Optimal Data MiXture (TREX), a regression-based framework that efficiently predicts the optimal data mixture for tokenizer training. TREX trains small-scale proxy tokenizers on random mixtures, gathers their compression statistics, and learns to predict compression performance from data mixtures. This learned model enables scalable mixture search before large-scale tokenizer training, mitigating the accuracy-cost trade-off in multilingual tokenizer design. Tokenizers trained with TReX's predicted mixtures outperform mixtures based on LLaMA3 and uniform distributions by up to 12% in both inand out-of-distribution compression efficiency, demonstrating strong scalability, robustness, and practical effectiveness.