An example method is provided and includes identifying an active speaker of a video session; analyzing a signal from an originating endpoint associated with the active speaker; identifying a target participant with whom the active speaker seeks to interact; and providing a notification to the target participant that alerts the target participant that the active speaker is seeking to interact with the target participant. In more particular embodiments, the identifying of the target participant includes detecting a gaze of the active speaker; and identifying a target screen to which the gaze is directed.