Large language models (LLMs) excel in many natural language processing (NLP) tasks. However, since LLMs can only incorporate new knowledge through training or supervised fine-tuning processes, they are unsuitable for applications that demand precise, up-to-date, and private information not available in the training corpora. This precise, up-to-date, and private information is typically stored in relational databases. Thus, a promising solution is to augment LLMs with the inclusion of relational databases as external memory. This can ensure the timeliness, correctness, and consistency of data, and assist LLMs in performing complex arithmetic operations beyond their inherent capabilities. However, bridging the gap between LLMs and relational databases is challenging. It requires the awareness of databases and data values stored in databases to select correct databases and issue correct SQL queries. Besides, it is necessary for the external memory to be independent of the LLM to meet the needs of real-world applications. We introduce a novel LLM-agnostic memory architecture comprising a database selection memory, a data value memory, and relational databases. And we design an elegant pipeline to retrieve information from it. Besides, we carefully design the prompts to instruct the LLM to maximize the framework's potential. To evaluate our method, we compose a new dataset with various types of questions. Experimental results show that our framework enables LLMs to effectively answer database-related questions, which is beyond their direct ability.