In this paper, we propose a general model to evaluate the equivalent magnetic noise for an off-diagonal giant magneto-impedance (GMI) sensor utilizing a software-defined radio (SDR) as a digital receiver. Based on this SDR approach, an analog-to-digital conversion (ADC) of the voltage induced by the sensing element is directly performed. The signal processing is digitally achieved in real time. It includes a digital quadrature demodulation, a decimation, and a filtering. The approach allows to give the key rules for quantifying the white noise level of this digital implementation. The voltage noise spectral density of the ADC and of each SDR stage is given. The white noise level expected by the modeling was in good agreement with the measurements. With a sensing element composed of a 400 turn coil wound around a co-rich GMI wire, equivalent magnetic noise levels of 220 and 4.2 pT/ $\sqrt {Hz}$ were obtained at 1 Hz and in the white noise region, respectively. The potential improvement of these performances, allowed by this digital conditioning, as well as limitations is also discussed.