Currently, companies apply existing asset discovery approaches in an ad hoc manner over asset repositories to find the right assets. To precisely identify the right assets, the discovery engine should acquire different types of knowledge regarding: (1) the created assets, (2) the involved application domains, (3) the adopted software ontologies, (4) the adopted matching approaches, and (5) users' contexts and goals. Then the discovery engine uses all these types of knowledge to find the right assets. Hence, we need a framework that is able to manage all these types of knowledge in a dynamic, machine-understandable, and context-sensitive manner. Therefore, this article proposes USTA an aspect-oriented knowledge management framework for reusable assets discovery. USTA enables companies to define and manage their software ontologies in an aspect-oriented manner. It also enables them to define their corresponding matching schemes. USTA enables users to define their goals, contexts, and their preferred matching policies along with their aspect-oriented queries. USTA uses all this information to dynamically create a customized discovery process for every query. Experimental results show that the dynamic and customized discovery approach adopted by USTA provides better matching precision when compared to existing discovery approaches that adopt a static discovery process for all queries.