5G shifted the paradigm from mere communication to in-network computing, so that networks have started applying the compute-and-forward paradigm. With the advent of the current vision of future communication networks (e.g., 6G), in-network intelligence also has become pivotal. Data analytics and their storage for continuous accurate learning and intelligent decision-making have become part of the communication. This explosion of data to be stored for unknown duration of time is going to stress the future communication infrastructure, which will be unable to achieve the targeted energy usage together with low-latency and reliability. This article presents a possible solution via data storage based on synthetic DNA. We further propose approaches for the implementation of DNA data storage into future communication networks. The focus is especially on the impact that DNA storage can have for storing the historic data of a network controlled by artificial intelligence for network automation and prediction of future network states (intelligent management). In this sense, DNA data storage can offer a unique opportunity to store efficiently and reliably large amounts of data, mined during network monitoring and traffic engineering.