The performance of magneto-impedance sensors to detect the presence and concentration of magnetic nanoparticles is investigated, using finite element calculations to directly solve Maxwell's equations. In the case of superparamagnetic particles that are not sufficiently magnetized by an external field, it is assumed that the sensitivity of the magneto-impedance sensor to the presence of magnetic nanoparticles comes from the influence of their magnetic permeability on the sensor impedance, and not from the stray magnetic field that the particles produce. The results obtained not only justify this hypothesis, but also provide an explanation for the discrepancies found in the literature about the response of magneto-impedance sensors to the presence of magnetic nanoparticles, where some authors report an increasing magneto-impedance signal when the concentration of magnetic nanoparticles is increased, while others report a decreasing tendency. Additionally, it is demonstrated that sensors with lower magneto-impedance response display larger sensitivities to the presence of magnetic nanoparticles, indicating that the use of plain, nonmagnetic conductors as sensing materials can be beneficial, at least in the case of superparamagnetic particles insufficiently magnetized in an external magnetic field.