In the Internet of Things paradigm, the total number of interconnected smart objects tends to increase in elevate rates in the next years, creating an overload of objects to be controlled and configured by the users themselves. Alternatively, context-aware discovery services have potential to minimize this problem by applying rules to determine which smart objects are more suitable for users, at a certain time. To help acquiring the contextual information, there are several context acquisition middlewares, e.g., LoCCAM, that creates abstraction layers which provides application a simple way to define and apply contextual discovery rules. This work proposes the CoAP-CTX, an extension of the built-in discovery service present in the CoAP protocol. Our approach aims to provide support to a context-aware discovery service of smart objects. The CoAP-CTX matches users' interest and context with the smart objects state data to retrieve most relevant smart objects to the user in this instant. Additionally, smart objects that are not of the user's interest go into an idle state, optimizing the network and battery usage. Experiments have shown that CoAP-CTX can decrease the total number of messages up to 80% in scenarios where a large number smart objects are presents in a generic environment, like working buildings. The overhead of the discovery latency shows a maximum discovery time increase of 1.5 seconds.