In Wi-Fi networks, Device-to-Device (D2D) communications aim to improve the efficiency of the network by supporting direct communication between users in close proximity. However, in a congested Wi-Fi network, establishing D2D connections through a locally managed self-organising approach will intensify the congestion and reduce the scalability of the solution. Therefore, a centralised management approach must be involved in orchestrating those actions to guarantee the sufficiency of D2D communications. In this paper, we propose a novel management framework for D2D communications in dense Wi-Fi networks. The proposed framework employs a Software-Defined Networking (SDN) based centralised controller in synergy with a novel Access Point (AP) channel assignment process. This framework is designed to proactively establish and manage D2D connections in Wi-Fi networks considering the available radio resources and the effect of the subsequent interference. Thus, improving the overall performance of the network and providing users with higher data rate. Through simulation, we validate the effectiveness of the proposed framework and demonstrate how D2D deployment considerably improves the Wi-Fi network efficiency especially when the data rate requirements are high. Furthermore, we show that our proposed framework achieves better performance than the widely deployed Least Congested Channel selection strategy (LCC).