Engineering light absorption in graphene has been the focus of intensive research in the past few years. In this paper, we show numerically that coherent perfect absorption can be realized in monolayer graphene in the near infrared range by harnessing resonances of dielectric nanostructures. The asymmetry of the structure results in different optical responses for light illuminated from the top side and the substrate side and enables asymmetric interferometric light-light control. The absorbed and scattered light exhibit interesting nonlinear behavior, allowing switching a strong optical signal output with a weak light. This work may stimulate potential applications including new types of sensors, coherent photodetectors and all-optical logical devices.