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Participants in a conversation must carefully monitor the turn-management (speaking and listening) willingness of other conversational partners and adjust their turn-changing behaviors accordingly to have smooth conversation. Many studies have focused on developing actual turn-changing (i.e., next speaker or end-of-turn) models that can predict whether turn-keeping or turn-changing will occur. Participants' verbal and non-verbal behaviors have been used as input features for predictive models. To the best of our knowledge, these studies only model the relationship between participant behavior and turn-changing. Thus, there is no model that takes into account participants' willingness to acquire a turn (turn-management willingness). In this paper, we address the challenge of building such models to predict the willingness of both speakers and listeners. Firstly, we find that dissonance exists between willingness and actual turn-changing. Secondly, we propose predictive models that are based on trimodal inputs, including acoustic, linguistic, and visual cues distilled from conversations. Additionally, we study the impact of modeling willingness to help improve the task of turn-changing prediction. To do so, we introduce a dyadic conversation corpus with annotated scores of speaker/listener turn-management willingness. Our results show that using all three modalities (i.e., acoustic, linguistic, and visual cues) of the speaker and listener is critically important for predicting turn-management willingness. Furthermore, explicitly adding willingness as a prediction task improves the performance of turn-changing prediction. Moreover, turn-management willingness prediction becomes more accurate when this joint prediction of turn-management willingness and turn-changing is performed by using multi-task learning techniques.