End-to-end speech language models increasingly represent user speech with speech tokens rather than relying exclusively on cascaded ASR--LLM--TTS pipelines. Although these tokens support expressive and low-latency spoken interaction, they may also preserve sensitive speaker characteristics. We investigate whether exposed speech tokens leak voiceprints and formulate this risk as a speaker inversion attack. We introduce Audio BERT (AuB), a trainable model that constructs token embeddings from discrete codebooks and aggregates them into speaker-sensitive representations, and propose SpInv, a two-stage inversion method built on AuB to recover embeddings in the space of an attacker-specified speaker encoder. We evaluate Moshi, Higgs3, Kimi-Audio, and Qwen3-Omni using speaker-disjoint protocols on the VoxCeleb dataset. Extensive experiments show that, with only three seconds of frontend output, SpInv achieves cosine similarities above 0.70 in the attacker-specified speaker-encoder space.