Conical intersections are formed when 2 or more electronic states become degenerate and give rise to ultrafast nonadiabatic processes such as radiation-less decay channels and geometric phase effects. The branching of nuclear wave packets near a conical intersection creates a coherent superposition of electronic states, which carries information about the energy difference of the involved states. X-ray Raman techniques have been proposed to observe the coherent superposition of the electronic states and to monitor the evolving electronic state separation. However, these techniques rely on the coherence generated as the wave packet passes through the conical intersection, and the electronic energy gap before the wave packet passes through the conical intersection is not tracked. In this paper, we theoretically demonstrate how a nonlinear Raman detection scheme can be used to gain further insight into the nonadiabatic dynamics in the vicinity of the conical intersection. We employ a combination of a resonant visible/infrared pulse and an off-resonant x-ray Raman probe to map the electronic state separation around the conical intersection. We demonstrate that this technique can achieve high contrast and is able to selectively probe the narrow electronic state separation around the conical intersection.