Itβs not supported right now but @looeee has already worked on this. His PR might be a good starting point:
Using compressed textures is an important feature and I believe three.js will pay more attention to this topic in the future. For now, providing platform independent texture compression is difficult since no format is supported on all platforms. That means, you have to generate multiple versions of the same texture and use the correct one for a specific device. Besides, the most promising format ASTC is still one of the worst supported standards.