Asymmetric image retrieval (AIR), which typically employs a compact model for the query side and a large model for the database server, has garnered significant attention in resource-constrained environments. While deep hashing methods have shown great potential in large-scale image retrieval, current attempts for the asymmetric image retrieval overlook the differences in quantization capabilities between query and gallery networks. In AIR, the conventional quantization scheme forces the outputs of small query models to approximate the discrete outputs of large models, imposing overly rigid and stringent constraints that severely limit the optimization of small query models. Furthermore, existing deep hashing methods for AIR necessitate labeled datasets from large models, which also limits their practical applicability. To this end, we reconsider the necessity of strict discretization in AIR and propose a novel asymmetric hashing method, named $\textbf{D}$eep $\textbf{C}$orrelation $\textbf{A}$lignment $\textbf{H}$ashing (DCAH). Rather than explicitly quantizing continuous query features to match discrete gallery representations, we distill the correlation across both models and introduce a $\textbf{C}$orrelation $\textbf{A}$lignment based $\textbf{Q}$uantization (CAQ) scheme, thereby implicitly accomplishing quantization. To preserve the similarity consistency between the query and gallery models, we further employ a correlation alignment-based knowledge distillation strategy which is intrinsically compatible with the CAQ. Notably, the proposed quantization scheme can function as a plug-and-play module that seamlessly integrates with existing AIR methods. Comprehensive evaluations on three real-world benchmark datasets demonstrate the effectiveness of the proposed quantization scheme CAQ, and also show that DCAH achieves state-of-the-art performance in asymmetric image retrieval scenarios. The open-source code is available at https://anonymous.4open.science/r/DCAH.