The use of network covert channels to improve privacy or support security threats has been widely discussed in the literature. As today, the totality of works mainly focuses on how to not disrupt the overt traffic flow and the performance of the covert channels in terms of undetectability and capacity. To not void the stealthiness of the channel, an important feature is the ability of restoring the carrier embedding the secret information into its original form. However, the development of such techniques mainly targets the domain of digital media steganography. Therefore, this paper applies the concept of reversible data hiding to storage network covert channels. To prove the effectiveness of our idea, a prototypical implementation of a channel exploiting IPv4 flows is presented along with its performance evaluation.