We investigate the integration of Large Language Models (LLMs) into query encoders to improve dense retrieval without increasing latency and cost, by circumventing the dependency on LLMs at inference time. SoftQE incorporates knowledge from LLMs by mapping embeddings of input queries to those of the LLM-expanded queries. While improvements over various strong baselines on in-domain MS-MARCO metrics are marginal, SoftQE improves performance by 2.83 absolute percentage points on average on five out-of-domain BEIR tasks.