We propose and demonstrate a modulation transfer protocol to increase the detection sensitivity of a Rydberg RF receiver to fields out of resonance from the transition between Rydberg levels. This protocol is based on a phase modulation of the control field used to create the Electromagnetically Induced Transparency signal. The nonlinear wave mixing of the multi-component coupling laser and the probe laser transfers the modulation to the probe laser, which is used for the RF-field detection. The measurements compare well with semi-classical simulations of atom–light interaction and show an improvement in the RF bandwidth of the sensor and an improved sensitivity of the response to weak fields.