Data streams are increasingly needed for different types of applications and domains, where dynamicity and data velocity are of foremost importance. In this context, research challenges raise regarding the generation, publication, processing, and discovery of these streams, especially in distributed, heterogeneous and collaborative environments such as the Web. Stream reasoning has addressed some of these challenges in the last decade, presenting a novel data processing paradigm that lays at the intersection among semantic data modeling, stream processing, and inference techniques. However, stream reasoning works have focused almost exclusively on architectures and approaches that assume an isolated processing environment. Therefore, they lack, in general, the means for discovering, collaborating, negotiating, sharing, or validating data streams on a highly heterogeneous ecosystem as the Web. Agents and multi-agent systems research has long developed principles and foundations for enabling some of these features, although usually under assumptions that require to be revised in order to comply with the characteristics of data streams. This paper presents a vision for a Web of stream reasoning agents, capable of sharing not only streaming data, but also processing duties, using collaboration and negotiation protocols, while relying on common vocabularies and protocols that take into account the high dynamicity of their knowledge, goals, and behavioral patterns.