Light scattering by semiconductor nanoparticles has been shown to be more complex than was believed until now. Both electric and magnetic responses emerge in the visible range. In addition, directional effects on light scattering of these nanoparticles were recently obtained. In particular, zero backward and minimum-forward scattering are observed. These phenomena are very interesting for several applications such as, for instance, optical switches or modulators. The strong dependence of these phenomena on the properties of both the particle and the surrounding medium can be used to tune them. The electrical control on the optical properties of liquid crystals could be used to control the directional effects of embedded semiconductor nanoparticles. In this work, we theoretically analyze the effects on the directional distribution of light scattering by these particles when the refractive index of a surrounded liquid crystal changes from the ordinary to the extraordinary configuration. Several semiconductor materials and liquid crystals are studied in order to optimize the contrast between the two states.